Grade 10 Circle Proofs Worksheet

This worksheet covers fundamental circle theorems and properties, requiring students to prove geometric relationships within circles.

Grade 10 Math GeometryCircle Proofs

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Includes

3 Short AnswerTrue / FalseFill in the BlanksMultiple Choice

Standards

CCSS.MATH.CONTENT.HSG.C.A.1CCSS.MATH.CONTENT.HSG.C.A.2CCSS.MATH.CONTENT.HSG.C.A.3

Topics

GeometryCircle ProofsTheoremsGrade 10 Math

8 sections · Free to use · Printable

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Grade 10 Circle Proofs Worksheet

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Read each question carefully and provide clear, logical proofs for each statement. Show all your work and state any theorems or postulates used.

1. In circle O, chord AB is perpendicular to chord CD at point E. Prove that arc AC is congruent to arc AD.

2. An angle inscribed in a semicircle is always a right angle.

True

False

3. A tangent to a circle is to the radius drawn to the point of tangency.

4. Given a circle with center O and an external point P. If PA and PB are tangents to the circle at points A and B respectively, prove that PA = PB.

5. Which of the following is true for a cyclic quadrilateral?

Opposite angles are supplementary.

All angles are acute.

Adjacent angles are complementary.

Diagonals are perpendicular.

6. Prove the alternate segment theorem: The angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.