Question

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

A
ABBD
B
ACDC
C
BDDC
D
ABAC

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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