CAT Practice : Coordinate Geometry

You are here: Home  CAT Questionbank   CAT Quant  Geometry: Triangles  Question 38
Radius of the circle inscribed inside a semi - circle

Circles

    Q.38: Two circles of radius 5 cm have a direct tangent PQ and an indirect tangent RS. Find the length of PQ if RS = 24 cm.
    1. 29 cm
    2. 13 cm
    3. 26 cm
    4. Cannot be determined due to lack of information

 

  • Correct Answer
    Choice (C). 26 cm

Detailed Solution

Let us draw the required diagram as:-

Since, OP = PQ and OP⊥PQ and O’Q⊥PQ
PQ = OO’
Now in △ORT and △O’ST
∠ORT = ∠O’ST
∠OTR = ∠STO’
∴ △ORT is similar to O’ST (AA)

=) RT = TS
Given RS = 24 cm
∴ RT = TS = 12cm
∴ OT = √((OR)2 + (RT)2 ) = √(52 + 22 ) = 13 cm = O’T
∴ OO’ = PQ = 13 +13 = 26 cm = (c) Ans.




Correct Answer: (C). = 26 cm



Our Online Course, Now on Google Playstore!

2IIM's App

Fully Functional Course on Mobile

All features of the online course, including the classes, discussion board, quizes and more, on a mobile platform.


Cache Content for Offline Viewing

Download videos onto your mobile so you can learn on the fly, even when the network gets choppy!

Get it on Google Play
Geometry is probably the most vital topic as far as CAT preparation is concerned. Geometry sets the stage for Trigonometry, Cogeo and Mensuration as well.