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In a triangle $A B C, A B = A C$ and D is a point on side AC such that $B C 2 = A C ⋅ C D .$ Is the condition “ $B D = B C$ ” true or false?

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True

False

answer is A.

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Detailed Solution

It is given that,

B C 2 = A C × C D B C A C = C D B C

Let us draw the figure for better understanding.
Question Image

We can write that,

Δ A B C & Δ B D C B C A C = C D B C

∠ C = ∠ C c o m m o n Δ A B C ~ Δ B D C

The side angle side property has been used to prove the similarity.
Now, we know that corresponding sides of similar triangles are proportional.

A B A C = B D B C A B A B = B D B C

1 = B D B C B D = B C

Hence the given statement is true i.e.,

.
Hence, the correct option is 1.

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