Q. 45.0( 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 AC2 = CD.BC

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

AB2 – BD2 = AC2 – CD2

AB2 – (BC – CD)2 = AC2 – CD2

AB2 – BC2 – CD2 + 2.BC.CD = AC2 – CD2

AB2 – BC2 + 2.BC.CD = AC2

Substituting the value of CD above, we get,

AB2 – BC2 + 2AC2 = AC2

AB2 + AC2 = BC2

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

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