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Questions and Answers
What is the value of x if 56 + x = 142?
What is the value of x if 56 + x = 142?
x = 86
Using Pythagoras' theorem, what is the radius OB if BM = 5 cm and OB = OA = x?
Using Pythagoras' theorem, what is the radius OB if BM = 5 cm and OB = OA = x?
x ≈ 5.83
How do you express the relationship between obtuse BOD and angle BAD?
How do you express the relationship between obtuse BOD and angle BAD?
obtuse BOD = 2 × BAD = 2α°
What value do you get for angle AOC if AOC + 250° = 360°?
What value do you get for angle AOC if AOC + 250° = 360°?
In triangle AOC, if the angles are x, x, and 70°, what is the value of x?
In triangle AOC, if the angles are x, x, and 70°, what is the value of x?
Given the equation 4x + 36 = 180, what is the value of x?
Given the equation 4x + 36 = 180, what is the value of x?
If y - 22 + y + 34 + y = 180, what is the value of y?
If y - 22 + y + 34 + y = 180, what is the value of y?
What is the approximate diameter FD of the circle if sin 56° = 5.5 / FD?
What is the approximate diameter FD of the circle if sin 56° = 5.5 / FD?
What is the value of angle BOC when BAC is 36°?
What is the value of angle BOC when BAC is 36°?
If angles ABC, ABO, and AOB form a triangle and ABC is a right angle, what is the value of angle AOB if angle ABC is 90°?
If angles ABC, ABO, and AOB form a triangle and ABC is a right angle, what is the value of angle AOB if angle ABC is 90°?
Given that ACD and ABD are angles on the same arc, what is their common value?
Given that ACD and ABD are angles on the same arc, what is their common value?
In triangle ABC, if the two angles are expressed as x and x + 14, what is the value of x?
In triangle ABC, if the two angles are expressed as x and x + 14, what is the value of x?
What is the relationship between angle ABC and angle AOC given that AOC measures 120°?
What is the relationship between angle ABC and angle AOC given that AOC measures 120°?
If angles CAB and CBA are both 38°, what is the value of x in triangle AABC?
If angles CAB and CBA are both 38°, what is the value of x in triangle AABC?
In triangle ABC, if angles ACB and ABC satisfy the equation α + β = 90°, what does this imply about triangle ABC?
In triangle ABC, if angles ACB and ABC satisfy the equation α + β = 90°, what does this imply about triangle ABC?
What relationship can be established between angles AOB and ACB through the circle?
What relationship can be established between angles AOB and ACB through the circle?
Flashcards
Angle at the center
Angle at the center
The angle formed by two radii of a circle that meet at the center of the circle.
Angle in a semi-circle
Angle in a semi-circle
The angle formed by two points on the circumference of a semicircle and the endpoints of the diameter is always 90 degrees.
Angles on same arc
Angles on same arc
Angles subtended by the same arc at the circumference of a circle are equal.
Angle between tangent and chord
Angle between tangent and chord
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Tangents from an external point
Tangents from an external point
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Angles in a triangle
Angles in a triangle
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Isosceles triangle
Isosceles triangle
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Alternate angles
Alternate angles
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Angle on the Same Arc
Angle on the Same Arc
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Radius-Tangent Theorem
Radius-Tangent Theorem
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Pythagorean Theorem
Pythagorean Theorem
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Exterior Angle of a Triangle
Exterior Angle of a Triangle
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Base Angles of Isosceles Triangle
Base Angles of Isosceles Triangle
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Chord of a Circle
Chord of a Circle
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Study Notes
Review Set 21 - Geometry of Circles
- Angle at the Centre: The angle at the centre of a circle is twice the angle at the circumference subtended by the same arc.
- Isosceles Triangles: In a circle, if two radii are equal, the triangle formed by connecting the centre and the endpoints of the radii is isosceles. Base angles of an isosceles triangle are equal.
- Angles in a Triangle: The sum of the angles in any triangle is 180 degrees.
- Angles in a Semi-Circle: An angle in a semi-circle is a right angle (90 degrees).
- Tangent and Chord: The angle between a tangent and a chord drawn from the point of tangency is equal to the angle subtended by the chord in the alternate segment.
- Tangents from an External Point: Tangents drawn from an external point to a circle are equal in length.
- Midpoint of a Chord: The perpendicular bisector of a chord passes through the centre of the circle.
Practice Test 21B
- Angles on Same Arc: Angles subtended by the same arc at the circumference are equal
- Exterior Angle of a Triangle: The exterior angle of a triangle is equal to the sum of the two opposite interior angles.
- Pythagorean Theorem: In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. a² + b² = c².
- Radii: Radii of a circle are all equal in length.
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