Xavier Aptitude Test 2014 Paper

Question : 58 of 103

Marks: +1, -0

There are two circles C1 and C2 of radii 3 and 8 units respectively. The common internal tangent, T, touches the circles at points

P_1

and

P_2

respectively. The line joining the centers of the circles intersects T at X. The distance of X from the center of the smaller circle is 5 units. What is the length of the line segment

P_1 P_2

≤ 13
> 13 and ≤ 14
> 14 and ≤15
> 15 and ≤ 16
> 16

Validate

Solution:

\ {P}_{1} \ {X}=\√{25-9}=4

\Δ{PP}_{1} \ {X} ∼{BP}_{2} \ {X}

⇒ A

P_1

/ B

P_2

P_1

P_2

\⇒ 3 / 8=4 /{P}_{2} \ {X}

{P}_{2} \ {X}=10.66

{P}_{1} {P}_{2}= {P}_{1} \ {X}+ {P}_{2} \ {X}=14.66

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