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Question

In a right angled triangle $$ABC, AD$$ is perpendicular to the hypotenuse $$BC$$ then $$AD^2$$ is equal to:


A
ABBD
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B
ACDC
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C
BDDC
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D
ABAC
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Solution

The correct option is C $$BD\cdot DC$$
$$AD$$ is $$\bot $$ to $$BC$$ where $$BC$$ is hypotenuse.

In $$\triangle ABC$$,

$${ AB }^{ 2 }+{ AC }^{ 2 }={ BC }^{ 2 }$$

The area of triangle is either $$\dfrac { 1 }{ 2 } AB\times AC$$ or $$\dfrac { 1 }{ 2 } BC\times AD$$ 

When we equate both,
$$AB\times AC=BC\times AD$$

The perpenidcular $$AD$$ divides the base $$BC$$ into parts.
$$\therefore { AD }^{ 2 }=BD \times DC$$

Mathematics

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