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Question

In a triangle ABC, AB=AC and A=36. If the internal bisector of C meets AB at point D, then

A
AD = BC
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B
AD = AC
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C
AD = AB
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D
AB = AC = BC
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Solution

The correct option is A AD = BC
Given: A=36 and AB=AC
Since, AB=AC
B=C=x (Isosceles triangle property)
In ABC
A+B+C=180
36+x+x=180
x=72
B=C=72
Since, CD bisects C
BCD=ACD=12C=36
Now, In BDC,
B+BCD+BDC=180 (Angle sum property)
72+36+BDC=180
BDC=72
Thus, BDC=B=72
Hence, BC=AD (Isosceles triangle property)

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