Q. 25.0( 1 Vote )

# <img width="35" h

Answer : Since AD is the altitude to BC,

BDA = CDA = 90°

So, Δ ABD and Δ ACD are right angle triangles.

Using Pythagoras theorem,

AB2 = BD2 + AD2 ...... (1)

And, AC2 = AD2 + DC2 ...... (2)

It is given that AD2 = BD.DC …… (3)

From equation (1) and (3), we get,

AB2 = BD2 + BD.DC

AB2 = BD(BD + DC) = BD. BC Now, from equation (2) and (3),

AC2 = BD.DC + DC2

AC2 = DC (BD + DC)

AC2 = DC(BC) Also, BC = BD + DC,

Substituting the value of BD and DC in above equation, we get, BC2 = AB2 + AC2

So, by the converse of Pythagoras Theorem, we can say that BAC is a right angle.

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