Grade 12 Circle Proofs Worksheet

Grade 12 Circle Proofs Worksheet

Read each question carefully and provide clear, logical proofs for the statements. Show all your work.

1. Given a circle with center O and a point P on the circle. A line 'l' is tangent to the circle at P. Prove that the radius OP is perpendicular to the tangent line 'l'.

2. Prove that the measure of an inscribed angle is half the measure of its intercepted arc. Consider the case where the center of the circle lies on one side of the inscribed angle.

3. The angle formed by a tangent and a chord drawn from the point of contact is equal to the angle in the  .

4. If two tangents are drawn to a circle from an external point, then the lengths of the tangent segments from the external point to the points of tangency are  .

5. A chord that passes through the center of a circle is called a diameter.

6. The perpendicular from the center of a circle to a chord bisects the chord.

7. Prove that the opposite angles of a cyclic quadrilateral are supplementary.