SSC CGL 16 Aug 2015 Shift 2 Paper

Question : 142 of 200

Marks: +1, -0

AC is transverse common tangent to two circles with centres P and Q and radii 6 cm and 3 cm at the point A and C respectively. If AC cuts PQ at the point B and AB = 8cm then the length of PQ is :

13 cm
12 cm
10 cm
15 cm

Validate

Solution:

In D APB and D BCQ,
∠ PAB = ∠ BCQ = 90°
∠ PBA = ∠ QBC
By AA – similarity,
Δ APB ~ Δ BQC
∴

{AB}/{BC}

{AP}/{QC}

⇒

8/{BC}

6/3

⇒ BC =

{8×3}/6

= 4 cm
∴ PQ =

√{AC^2+(r_1+r_2)^2}

√{(8+4)^2+(6+3)^2}

√{12^2+9^2}

√{144+81}

√{225}

= 15 cm

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