Finding area of circle based off of distance between midpoints of two chords

Question

Chords AB and AC in a circle have lengths of 6 and 8 respectively. If the distance between the midpoints of AB and AC is 5, what is the area of the circle O?

Answer 1

Draw a diagram and label.

Label the midpoint of AB as D, and the midpoint of AC as E.

AD = 3, AE = 4, and DE = 5

Triangle ADC is a right triangle with ∠A = 90°.

BC is a diameter of circle O. BC = 10, by similar triangles.

The radius is 5 

 

A = πr²

A = 25π