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Question

If AD is external bisector of A which meets BC at D and CE || DA. Then, which of the following is true?

A
BDCD=ABAC
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B
BDCE=ABAD
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C
Both (a) and (b)
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D
None of these
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Solution

The correct option is A BDCD=ABAC

Given, AD bisects A externally and CE || AD

2=4 and 3=1 [BK, CA respectively being the transversal]
But 1=2 [Since AD bisects A externally]
3=4
In ΔACE,
3=4AE=AC ...(i) [ sides opposite to equal angles in a triangle are equal]
Now, in Δ BAD, EC||AD
BDCD=BAEA [by basic proportionally theorem]
BDCD=ABAC [from Eq. (i)]
Hence option A is the correct option.

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