Circle Geometry Review PDF

### **Circle Geometry Review** **Page 1:** 7. Study the figure below. What theorem represents by circle A? - [Image of a circle with points A, B, C, D, E marked on it.] In a circle, two minor arcs are congruent if and only if their corresponding central angles are congruent. **Page 2:** 1. Whe...

### **Circle Geometry Review** **Page 1:** 7. Study the figure below. What theorem represents by circle A? - [Image of a circle with points A, B, C, D, E marked on it.] In a circle, two minor arcs are congruent if and only if their corresponding central angles are congruent. **Page 2:** 1. When two secants intersect outside the circle, an angle will form. Find the measure of the angle formed by the two secants. - [Image of a circle with two secants intersecting outside the circle. The angle formed by the secants is marked with "x" and the central angle is marked 27 degrees. Another central angle is marked as 125 degrees and an external angle is marked 49 degrees.] **Page 3:** 2. You are tasked to count the number of secant segments in the circle Q below, how many secant segments are there? - [Image of circle with points M, N, O, P, Q, R, S marked on it.] 2 secant segments **Page 4:** 3. In circle A arc CD measures 100° and arc BE measures 30°, how will you find the measure of ∠CFD? - [Image of circle A with points C, D, E, F marked on it.] Half the difference of the measures of arc CD and BE. **Page 5:** 1. The theorem states that if two chords of a circle intersect, then the product of the measures of the segments of one chord is equal to the product of the measures of the segments of the other chord. - [Image of a circle with points A, D, N, L, S on it.] Write the equation based on the given theorem and figure below. SA•AN=DA•AL **Page 6:** 2. The theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the length of the tangent segment is equal to the product of the lengths of the secant segment and its external secant segment. - [Image of a circle with points C, O, N, Y on it.] CO² = YO•NO **Page 7:** 3. AB and CD intersects at point A. If CD = 12 and AC = 4, what is the measure of AB? - [Image of a circle with points A, B, C, D, E on it and line segments AC = 4 and CD = 12.] **Page 8:** 1. In a circle with center O, the radius is 10cm. A central angle AOB subtends a sector AOB. If the arc AB is 60°, what is the area of the sector AOB? - [Image of a circle with points A, B, O and arc AB marked as 60 degrees] 52.36 cm² **Page 9:** 1. Catherine designed a pendant. It is a regular hexagon set in a circle. Suppose the opposite vertices are connected by line segments and meet at the center of the circle, what is the measure of each angle formed at the center? - [Image of a regular hexagon inscribed in a circle. This is the shape of a pendant.] 60° **Page 10:** 2. A circular garden has two paths that intersect outside the garden. One intercepted arc measures 240 degrees, and the other measures 120 degrees. What is the angle formed by the two paths? - [Image of a circle with two secants intersecting outside the circle.] 60° **Page 11:** 3. A circular children’s park has 3 different pathways from the main road. If the distance from the main road to Gate 2 is 70m and the length of the pathway from Gate 2 to the exit is 50m, how far from the main road is gate 1? - [Image of a circular park with three pathways marked as Gate 1, Gate 2 and Exit.] √8400 or 20√21 **Page 12:** 1. What equation/ formula can be used to find the distance between any pair of points on the coordinate plane? d = √(x2-x1)² + (y2-y1)² **Page 13:** 2. The coordinates of Lito’s house are A(2, 3) and the coordinates of Boby’s house are B(8, 5). They need to find the exact midpoint of the line segment that connects their two houses to determine the best meeting spot. What are the coordinates of the midpoint of the line segment connecting their houses? (5, 4) **Page 14:** 3. Mang Kikos farm is triangular in shape. The piggery (P), chicken house (O) and goats barn (G) are located at P(-4, 0), C(0, 4) and G(4, 0) respectively. How far is the piggery from the chicken house? √32 or 4√2 **Page 15:** 4. A delivery truck is travelling between two locations. The first location is represented by the coordinates A(3, 4). The second location is represented by the coordinates B(7, 1). What is the distance between location A and location B? 5 units **Page 16:** 1. You are designing a circular park with a fountain in the center. The center of the fountain is located at point (0, 0) on a coordinate grid, and the fountain has a radius of 5 meters. What is the equation that represents the boundary of the fountain? x²+y²=25 **Page 17:** 2. A lighthouse has a light that shines in a circular pattern. The center of the light beam is located at point (7, -1), and the beam has a radius of 15 meters. Which equation represents the boundary of the light's beam? (x-7)²+(y+1)²=225 **Page 18:** 3. A drone flies in a circular path represented by the equation x²+y²=49. What is the center and the radius of the drone’s flight path? center: (0, 0) r: 7 **Page 19:** 4. A city map shows a circular park with an equation given as represented (x+7)²+(y+8)²=64. What is the center and the radius of the park? center: (-7, -8) r : 8 **Page 20:** 5. A circular pond’s equation is (x+5)²+(y-7)²=81. You need to verify if the point (4, 7) lies on the edge of the pond. Does point ( 4, 7) lie on the edge of the pond? Yes, because substituting (4, 7) into the equation equals 81. **Page 21:** 7. Given the figure below, write the center and radius form of the circle. - [Image of a circle graphed on a coordinate plane. The center of the circle is at (3, -2) and the radius is 4.] (x-3)²+(y+2)²=16 **Page 22:** 8. Graph the equation of a circle x²+y²+10x-8y-8=0? - [Image of a graph on a coordinate plane showing a circle. The center of the circle is at (-5, 4) and the radius is 7.] **Page 23:** 3. To properly analyze the function, you need to express it in its standard form. The polynomial function y=5x²+2x³-x⁴+3 has 4 terms, what is its standard form? y=-x⁴+2x³+5x²+3 **Page 24:** 3. To properly analyze the function you need to express it in its standard form. The polynomial function y=5x²+2x³-x⁴+3 has 4 terms, what is its standard form? y=-x⁴+2x³+5x²+3 **Page 25:** 4. A polynomial function P(x) = x³-3x²-4x+12 is graphed. A student observes that the function intersects the x-axis at x=-2, 2 and 3. Write the factored form of the given polynomial. (x+2)(x-2)(x-3) **Page 26:** 1. In graphing polynomial functions, x and y intercepts play a very important role. What are the x-intercepts of the given graph? - [Image of a polynomial function graphed on a coordinate plane. Four x-intercepts are marked on the graph.] (-4, 0) (-2, 0) (1, 0) (4, 0) **Page 27:** 2. The graph of a polynomial function is a smooth curve. Graph y = x⁴-5x²+4. - [Image of a polynomial function graphed on a coordinate plane.] **Page 28:** 3. Your friend Matthew asks your help in drawing a rough sketch of the graph of y = -(x²+1)(2x+3). How will you show the behavior of the graph? The graph comes up from the extreme left and goes down to the extreme right. **Page 29:** 4. Drake needs to determine which equation best represents the graph on the right. What equations will accurately represent the graph? - [Image of a polynomial function graphed on a coordinate plane.] P(x) = -x³+3x² + 4x - 12 **Page 30:** 1. The volume of the box is given by V(x) = 2x³+7x²+3x. What expression represents the missing width? - [Image of a box with length x+3, width 2x+1, and height "x" marked on it.] **Page 31:** 2. The number of tourists who visited Magallanes can be modeled by the function v(t) = 2t⁴ + 10t³-2t+5 where v(t) is the number of visitors and t is the number of months. How many visitors visited Magallanes on the 5th month? 2495 visitors/tourists **Page 32:** 3. You are the newly hired Administrative Assistant of MinStop convenience store in Daang Amaya. Your task is to analyze revenue for the past 10 years of its operation. Its annual revenue R (in millions) can be approximated by the function R(t) = 100(t⁴ + 12t³ -77t² + 600t + 13000) where t is the number of years since the store opened. What is the revenue of the store on its 3rd year of operation? ₱1,451,200 **Page 33:** 1. The chords, arcs, central and inscribed angles of a circle have relationships with one another. State whether the following is true or false. II. The diameter of a circle is half its radius. false **Page 34:** 1. The chords, arcs, central and inscribed angles of a circle have relationships with one another. State whether the following is true or false. II. The sum of all central angles in a circle is 360°. true **Page 35:** 1. The chords, arcs, central and inscribed angles of a circle have relationships with one another. State whether the following is true or false. IV. The degree measure of a central angle is half the degree measure of its intercepted arc. false **Page 36:** 1. The chords, arcs, central and inscribed angles of a circle have relationships with one another. State whether the following is true or false. V. The measure of an angle inscribed in a circle is twice the measure of the central angle intercepting the same arc. false **Page 37:** 1. The chords, arcs, central and inscribed angles of a circle have relationships with one another. State whether the following is true or false. VI. The measure of an inscribed angle is one half the measure of the arc intercepted by this angle. true **Page 38:** 1. The chords, arcs, central and inscribed angles of a circle have relationships with one another. State whether the following is true or false. VII. The degree measure of a major arc is equal to 360° minus the measure of the minor arc with the same endpoints. true **Page 39:** 2. In the circle, points A, B, and C lie on the circumference. If the measurement of arc AC is 50°. Find the measures of ∠ABC. - [Image of a circle with points A, B, C on it, ∠ABC marked as 25 degrees and arc AC marked as 50 degrees.] 25° **Page 40:** 3. What relationship among arcs and angles best describes the item number 2? - [Image of a circle with points A, B, C on it, ∠ABC marked as 25 degrees.] The measure of an inscribed angle is one half the measure of the arc intercepted by this angle. **Page 41:** 5. What relationship among arcs and angles best describes the term No. 4? - [Image of a circle with points A, B, C, D on it. ∠ACB marked as 74 degrees.] The degree measure of a major arc is equal to 360° minus the measure of the minor arc with the same endpoints. 360°-70° **Page 42:** In ⊙A, ∠LAM = 45°, ∠HAG = 30°, and ∠KAH is a right angle. - [Image of a circle with points A, G, H, J, K, L, M on it.] 1. What is the degree measure of arc KLM? 135° **Page 43:** In ⊙A, ∠LAM = 45°, ∠HAG = 30°, and ∠KAH is a right angle. - [Image of a circle with points A, G, H, J, K, L, M on it.] 2. What is the degree measure of arc LMG? 150° **Page 44:** In ⊙A, ∠LAM = 45°, ∠HAG = 30°, and ∠KAH is a right angle. - [Image of a circle with points A, G, H, J, K, L, M on it.] 3. What is the degree measure of ∠KAM? 135° **Page 45:** Aiza measures the following: AB and CD are chords. ∠AOB is a central angle that measures 120°. ∠ACB is an inscribed angle that intercepts the same arc as ∠AOB. - [Image of a circle with points A, B, C, D, O on it. ∠AOB marked as 120 degrees.] 4. What is the measure of the inscribed angle ∠ACB if the central angle ∠AOB = 120°? 60° **Page 46:** Aiza measures the following: AB and CD are chords. ∠AOB is a central angle that measures 120°. ∠ACB is an inscribed angle that intercepts the same arc as ∠AOB. - [Image of a circle with points A, B, C, D, O on it. ∠AOB marked as 120 degrees.] 5. If arcs AB and CD have equal measures, what can you conclude about the lengths of chords AB and CD? congruent **Page 47:** 6. A quadrilateral is inscribed in a circle. The measure of ∠A is (4x+9)°, the measure of ∠C is (3x+3)°. Since opposite angles of an inscribed quadrilaterals add up to 180°. Find the value of x. - [Image of circle with quadrilateral inscribed in it. ∠ A marked as 4x+9 and angle C marked 3x+3] 24