Grade 9 Circle Theorems Worksheet
Explore and apply key circle theorems including tangent-radius theorem, angles in a semicircle, and cyclic quadrilaterals.
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Grade 9 Circle Theorems Worksheet
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Read each question carefully and answer to the best of your ability. Show all your work for full credit.
1. In a circle, the angle subtended by an arc at the center is the angle subtended by the same arc at any point on the remaining part of the circle.
equal to
half of
twice
one-third of
2. ANGLE AT CENTRE THEOREM: In the circle with center O, if angle AOB = 80°, what is the measure of angle ACB?
40°
80°
160°
20°
1. The angle in a semicircle is a angle.
2. The tangents from an external point to a circle are in length.
3. The sum of opposite angles of a cyclic quadrilateral is degrees.
1. A tangent to a circle is perpendicular to the radius at the point of tangency.
True
False
2. All angles subtended by the same arc in the same segment of a circle are equal.
True
False
1. In the circle with center O, AB is a diameter and C is a point on the circumference. If angle BAC = 35°, find angle ABC.
2. A quadrilateral ABCD is inscribed in a circle. If angle A = 70° and angle B = 95°, find angle C and angle D.
Match each circle theorem with its description.
1. Tangent-Radius Theorem
a. The angle subtended by an arc at the center is double the angle subtended by the same arc at any point on the remaining part of the circle.
2. Angle at Centre Theorem
b. A tangent to a circle is perpendicular to the radius at the point of tangency.
3. Angles in the Same Segment
c. The angle in a semicircle is a right angle.
4. Angle in a Semicircle
d. Angles subtended by the same arc in the same segment of a circle are equal.
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