Math

Congruent Chord Problem Set

1) Two circles intersect and have a

common chord that is 16 cm long. The

centers are 21 cm apart. If the radius

of one circle is 10 cm, what is the radius

of the other circle?

2) What is the diameter of the circle?

3) A 16 x 12 rectangle is inscribed in a

circle. Find the radius of the circle.

4) In circle O, if AB = 8, find OA.

5) In circle P, 𝑃𝐸̅̅ ̅̅ ≅ 𝑃𝐹,̅̅ ̅̅ ̅ 𝐴𝐸 = 8 + 𝑥 2, 𝐶𝐷 = 4𝑥 2 − 14𝑥. If 𝑥 < 0, find CD.

6) An equilateral triangle with a

perimeter of 24√3 is inscribed in a circle. Find the radius of the circle.

7) Find the area of a circle if a 16-unit

chord is 6 units from the center of the

circle.

45°

O

B A

D

C

B

A

P

E F

8) In circle P, let 𝐴𝐵 = 8𝑥 + 2𝑦, 𝐹𝐷 = 6𝑥 + 4𝑦 − 1 , 𝐸𝑃 = 2𝑥 − 𝑦, and 𝐹𝑃 = 𝑦 + 4𝑥 − 3. Find the diameter of the circle.

9) A circle is given as the equation (𝑥 + 3)2 + (𝑦 − 3)2 = 25. A chord on the circle is drawn from A (1, 6) and B (-3, -2). What is the distance from the center of the circle to the

chord? Give an exact solution.

D

C

B

A

P

E F