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Quantitative Aptitude

Triangles

In the given ...

Question

In the given figure, two circles are inscribed inside two adjoining triangles.

Given: PR=12, RV=18, PV=10. Find TV.

A

8

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B

12

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C

16

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D

10

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Solution

The correct option is A
8

Let ST=TM=TU=x; UV=VW=y.

Then RS= 18-(2x+y); PW=10-y=PM=PQ.

PR=RQ+PQ= 18-(2x+y)+ (10-y)=12; $\Rightarrow$ x+y=8. Now, TV=TU+UV=x+y. Hence TV=8.

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