Question

△ABC is inscribed in a circle such that vertices A and B lie on a diameter of the circle. If the length of the diameter of the circle is 13 and the length of chord BC is 5, find length AC.

The length AC is

Answer 1

AC=12

Explanation:

If vertices A and B lie on a diameter of the circle means that angle of triangle on the vertice C is 90, si this is right triangle. Now we can use Pitagora’s theorem to find AC.

AB^2=AC^2+BC^2

13^2=AC^2+5^2

169=AC^2+25

AC^2=169-25=144

AC=12