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Question

In the given figure, AB = AC, A=48 and ACD=18. Then which of the given options is correct?


A
BC = BD
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B
BC = CD
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C
BD = DC
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D
BC = 2 BD
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Solution

The correct option is B BC = CD

In ABC, BAC+ACB+ABC=180
48+ACB+ABC=180
But ACB=ABC ( Given, AB = AC and angles opposite to equal sides of a triangle are equal).
2ABC=18048
i.e., ABC=66 (i)
ACB=66
ACD+DCB=66
DCB=6618 (ACD=18)
DCB=48 (ii)
Now, in DCB,
DBC=66
(from (i), as DBC=ABC)
DCB=48 (from (ii))
BDC=1804866=66
BDC=DBC
Then, BC = CD (sides opposite to equal angles are equal)


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