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Two circles with radius of 4.5 cm and 12.5 cm respectively touch externally. If a tangent, common to both the circles, touches them at points P and Q respectively, find the length of PQ:

This question was previously asked in
OSSC Soil Conservation Extension Worker Official Paper II (Held on 22nd Oct 2017)
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  1. 12.5 cm
  2. 14.0 cm
  3. 15.0 cm
  4. 17.0 cm
  5. 21.5 cm

Answer (Detailed Solution Below)

Option 3 : 15.0 cm

Detailed Solution

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Solution:

F1 Shubanshi.P 24-09-20 Savita D2

If we drop a perpendicular on C2Q from C1 and name it R

Then, C1R = PQ

C2R = 12.5 - 4.5 = 8 cm

Now, 

C1C22 = C2R2 + PQ2

(12.5 + 4.5)2 = 82 + PQ2

PQ2 = 225

∴ PQ = 15 cm

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Latest OSSC Soil Conservation Extension Worker Updates

Last updated on Apr 9, 2025

-> OSSC Soil Conservation Extension Worker Merit List has been released for Prelims (2023 cycle). 

-> A total number of 324 Vacancies have been announced for the post of Soil Conservation Extension Worker under the Directorate of Soil Conservation and Watershed Development.

-> Eligible candidates had registered from 27th November 2024 to 26th December 2024. The applications for the post will be accepted in online mode only.

-> Candidates must refer to the OSSC Soil Conservation Extension Worker Previous Year Papers to analyze the trend of the questions for the examination. 

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