Podcast
Questions and Answers
Intersecting Chords Theorem: The two lines are chords of the circle and intersect inside the circle. In this case, we have $CE \cdot AE = BE \cdot _____$.
Intersecting Chords Theorem: The two lines are chords of the circle and intersect inside the circle. In this case, we have $CE \cdot AE = BE \cdot _____$.
DE
As shown in the figure, in Circle O, two chords AB and CD intersect at P. Given that PA = 3 cm, PB = 4 cm, and PC = 2 cm, then find the length of PD.
As shown in the figure, in Circle O, two chords AB and CD intersect at P. Given that PA = 3 cm, PB = 4 cm, and PC = 2 cm, then find the length of PD.
6 cm
As shown below, in Circle O, chord AB and radius OC intersect at M. Chord DD' is the extension of OC through the center. Suppose that $OM = MC$. Given that AM = 1.5 and BM = 4, find the length of OC.
As shown below, in Circle O, chord AB and radius OC intersect at M. Chord DD' is the extension of OC through the center. Suppose that $OM = MC$. Given that AM = 1.5 and BM = 4, find the length of OC.
$2\sqrt{2}$
Tangent-Secant Theorem: One line is tangent to the circle while the other is a secant. In this case, we have $AB^2 = BC \cdot _____$. (Where AB is the tangent length, BC is the external secant segment length, and BD is the total secant length).
Tangent-Secant Theorem: One line is tangent to the circle while the other is a secant. In this case, we have $AB^2 = BC \cdot _____$. (Where AB is the tangent length, BC is the external secant segment length, and BD is the total secant length).
As shown in the figure below, two circles intersect at C and D. AB is the common external tangent of the two circles. Let M be the intersection of AB and the common chord CD extended. If AB = 12 and CD = 9, then find the length of MD.
As shown in the figure below, two circles intersect at C and D. AB is the common external tangent of the two circles. Let M be the intersection of AB and the common chord CD extended. If AB = 12 and CD = 9, then find the length of MD.
As shown below, PT is tangent to a circle with center O at T, and PAB is a secant line that intersects the circle at A and B. Line segment CT intersects PAB at D. Given that CD = 2, AD = 3 and BD = 4, find the length of PB. Assume D is between A and B, and B is between P and A.
As shown below, PT is tangent to a circle with center O at T, and PAB is a secant line that intersects the circle at A and B. Line segment CT intersects PAB at D. Given that CD = 2, AD = 3 and BD = 4, find the length of PB. Assume D is between A and B, and B is between P and A.
Intersecting Secants Theorem: Both lines are secants of the circle and intersect outside of it. In this case, we have $CB \cdot CA = CD \cdot _____$. (Where CB and CD are external secant segments, and CA and CE are total secant segments).
Intersecting Secants Theorem: Both lines are secants of the circle and intersect outside of it. In this case, we have $CB \cdot CA = CD \cdot _____$. (Where CB and CD are external secant segments, and CA and CE are total secant segments).
As shown below, given a point P and a circle, draw two lines through P that intersect the circle. Secant PAB intersects at A and B. Secant PCD intersects at C and D. If PA = 3, AB = 2, and PC = 2, then find the length of PD.
As shown below, given a point P and a circle, draw two lines through P that intersect the circle. Secant PAB intersects at A and B. Secant PCD intersects at C and D. If PA = 3, AB = 2, and PC = 2, then find the length of PD.
As shown in the figure, P is a point outside of Circle O. The line segment OP intersects Circle O at A. Secant PC intersects Circle O at B and C, such that P-B-C is the order. It is given that PB = BC. Given that OA = 5 (radius) and that PA = 2, find the length of PC.
As shown in the figure, P is a point outside of Circle O. The line segment OP intersects Circle O at A. Secant PC intersects Circle O at B and C, such that P-B-C is the order. It is given that PB = BC. Given that OA = 5 (radius) and that PA = 2, find the length of PC.
As shown in the figure, P is a point outside the circle O, and the secant PAB intersects Circle O at points A and B (P-A-B order). If PA = 4, PB = 6, and PO = 7 (distance from P to the center O), then what is the radius of Circle O?
As shown in the figure, P is a point outside the circle O, and the secant PAB intersects Circle O at points A and B (P-A-B order). If PA = 4, PB = 6, and PO = 7 (distance from P to the center O), then what is the radius of Circle O?
Given the configuration in the figure involving point A outside multiple circles, tangent AB to circle Q, tangent AC to circle S, and intermediate secants ADE and AFG such that $AD \cdot AE = AF \cdot AG$. What is the relationship between the lengths of the tangent segments AB and AC?
Given the configuration in the figure involving point A outside multiple circles, tangent AB to circle Q, tangent AC to circle S, and intermediate secants ADE and AFG such that $AD \cdot AE = AF \cdot AG$. What is the relationship between the lengths of the tangent segments AB and AC?
Flashcards
Power of a Point Theorem
Power of a Point Theorem
A theorem relating lengths of line segments created when lines intersect a circle.
Intersecting Chords Theorem
Intersecting Chords Theorem
If two chords intersect inside a circle, the product of the segments of one chord equals the product of the segments of the other chord.
Tangent-Secant Theorem
Tangent-Secant Theorem
If a tangent and a secant are drawn from an external point to a circle, then the square of the tangent is equal to the product of the secant and its external segment.
Intersecting Secants Theorem
Intersecting Secants Theorem
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