Question

In figure, ∠BAC = 90° and AD ⊥ BC. Then, BD . CD = ______.

Answer 1

In figure, ∠BAC = 90° and AD ⊥ BC. Then, BD . CD = AD².

Explanation:

In right triangle ABC (∠BAC = 90°) the segment AD is the altitude to the hypotenuse BC. The three triangles ABD, ADC and ABC are similar, and from those similarities one gets the standard altitude-to-hypotenuse relation AD² = BD·DC.