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XAT 2014 — QA & DI Question 11

Simple EquationsEasy

There are two circles C1 and C2 of radii 3 and 8 units respectively. The common internal tangent, T, touches the circles at points P1 and P2 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 P1P2?

Answer & solution

Correct answer: > 14 and ≤ 15

  • A

    ≤ 13

  • B

    > 13 and ≤ 14

  • > 14 and ≤ 15

  • D

    > 15 and ≤ 16

  • E

    > 16

Solution

Let A, B be the centre of the two circles with radius 3cm, 8cm respectively.

​​​​​​​

AX = 5cm, AP1 = 3cm

Using Pythagoras theorem, P1X = 4cm

Now ∆ A P1X ≈ ∆ B P2X

⇒ A P1/ B P2 = P1X/ P2X

⇒ 3/8 = 4/ P2X

P2X = 10.66

P1 P2 = P1X + P2X = 14.66

Hence, option (c).

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XAT 2014 QA & DI Q11: There are two circles C 1 and C 2 of radii 3 and 8 units respectively. The common internal tangent, T, touches — Solution | TheCATExam