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.
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"
Choice C is the correct answer.
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