CAT Quantitative Aptitude Questions | Geometry Questions for CAT - Triangles

The question is from the topic circles. It discusses about two circles and their direct and indirect tangents. CAT Geometry questions are heavily tested in CAT exam. Make sure you master Geometry problems. We have to find out the length of the direct tangent given the length of the indirect tangent.

Question 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

Explanatory Answer

Method of solving this CAT Question from Circles:Draw the diagram, then you are through.

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)
∴ OR/OS = RT/TS => RT/TS = 5/5 = 1
=> 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

The question is "Find the radius of the circle"

Hence, the answer is 26 cm.

Choice C is the correct answer.