Question:
Two circles of radii 9 cm and 4 cm touch each other externally. A line touches the two circles at P and Q respectively. Then length of PQ, in cm, is
Two circles of radii 9 cm and 4 cm touch each other externally. A line touches the two circles at P and Q respectively. Then length of PQ, in cm, is
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For externally touching circles,
\[
PQ=\sqrt{(R+r)^2-(R-r)^2}=2\sqrt{Rr}.
\]
Updated On: Jun 15, 2026
- 13
- 10
- 11
- 12
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The Correct Option is D
Solution and Explanation
Concept:
For two circles touching externally, the length of the direct common tangent between the points of contact is
\[
PQ=\sqrt{d^2-(R-r)^2}
\]
where \(d\) is the distance between centers.
Step 1: Find the distance between centers. Since circles touch externally, \[ d=R+r=9+4=13 \]
Step 2: Apply the formula. \[ PQ=\sqrt{13^2-(9-4)^2} \] \[ PQ=\sqrt{169-25} \] \[ PQ=\sqrt{144} \] \[ PQ=12 \]
Step 1: Find the distance between centers. Since circles touch externally, \[ d=R+r=9+4=13 \]
Step 2: Apply the formula. \[ PQ=\sqrt{13^2-(9-4)^2} \] \[ PQ=\sqrt{169-25} \] \[ PQ=\sqrt{144} \] \[ PQ=12 \]
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