Exams › SSC CGL (Prelims) › General

A right triangle XYZ is inscribed in a circle with diameter 13 cm. An altitude from Y is drawn to the hypotenuse XZ. If the length of leg XY is 5 cm, what is the length of segment XH on the hypotenuse?

1. 25/13 cm
2. 37/11 cm
3. 2 cm
4. 7/12 cm

Correct answer: 25/13 cm

Solution

In a right triangle, the hypotenuse equals the diameter of the circumcircle, so \(XZ=13\) cm. Using the projection theorem, \(XY^2 = XZ \cdot XH\), hence \(25 = 13\cdot XH\), giving \(XH=\frac{25}{13}\) cm.

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