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Question

With usual notation, if r:R:r1=2:5:12, then A is equal to

A
60
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B
90
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C
30
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D
45
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Solution

The correct option is B 90
Given, r:R:r1=2:5:12
r=2k, R=5k, r1=12k
We know that
rr1=1as
212=1asas=56
Also, we have
Rr1=a2sinA×1stanA2
512=a2sinA×1stanA2
sinAtanA2=1
2sinA2cosA2sinA2cosA2=1
2(sinA2)2=1
sinA2=12
A2=45
A=90

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