Grade 12 Circle Theorems Worksheet
This worksheet covers key circle theorems including tangent-radius theorem, angles in a semicircle, cyclic quadrilaterals, and angles subtended by arcs, suitable for Grade 12 Geometry students.
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Grade 12 Circle Theorems Practice
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Read each question carefully and answer to the best of your ability. Show all your work where applicable. Diagrams are not necessarily drawn to scale.
1. In the diagram below, O is the center of the circle and AB is a tangent to the circle at point P. If the radius of the circle is 5 cm and OP is perpendicular to AB, what is the measure of angle OPA?
2. An angle inscribed in a semicircle is always a angle, measuring exactly degrees.
3. Which of the following statements is true for a cyclic quadrilateral?
Opposite angles are equal.
All angles are 90 degrees.
Opposite angles are supplementary.
Adjacent angles are complementary.
4. In the circle with center O, angle ∠AOB = 80°. What is the measure of angle ∠ACB, where C is a point on the major arc AB?
5. The angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.
True
False
6. Chords AB and CD intersect at point E inside a circle. If AE = 6 cm, EB = 4 cm, and CE = 3 cm, find the length of ED.
Match each description with the correct circle theorem.
7. The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.
a. Tangent-Chord Theorem
8. The angle between a tangent and a radius drawn to the point of contact is 90 degrees.
b. Angle at Centre Theorem
9. Opposite angles of a quadrilateral inscribed in a circle are supplementary.
c. Cyclic Quadrilateral Theorem
10. If two chords intersect inside a circle, the product of the segments of one chord is equal to the product of the segments of the other chord.
d. Intersecting Chords Theorem