Question

Let be H - the point of intersection of the heights of an acute-angled triangle ABC. From points A and C drawn tangents AK and CT to the circle drawn on the line segment BH as in diameter. Let be 15 and 17 - the lengths of these tangents. What is the smallest possible side length AC? In response, write down the square of the length AC.

Answer 1

AK² + AC² = CT²

15² + AC² = 17²

AC² = 289 - 225

AC² = 64

AC = 8

AC² = 64