Q. 35.0( 1 Vote )

# In ΔABC, <img wid

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 AB2 = BD.BC

From equation (1) and (2), we get,

AB2 – BD2 = AC2 – DC2

AB2 – BD2 = AC2 – (BC – BD)2

BC2 + BD2 – 2BC.BD = AC2 + BD2 – AB2

BC2 – 2BC (BD) = AC2 – AB2

Substituting the value of BD above, we get,

BC2 – 2(AB)2 = AC2 – AB2

BC2 = AB2 + AC2

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

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