Mathematics
In the given figure, AC is a transverse common tangent to two circles with centres P and Q and of radii 6 cm and 3 cm respectively. Given that AB = 8 cm, calculate PQ.
Circles
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Answer
Join AP and CQ.
AB ⊥ AP (∵ tangent at a point and radius through the point are perpendicular to each other.)
In right angled triangle PAB.
Considering △PAB and △BCQ,
∠A = ∠C (Each are equal to 90°)
∠ABP = ∠CBQ (Vertically opposite angles are equal)
△PAB ~ △BCQ by AA axiom.
Since triangles are similar hence, the ratio of their corresponding sides are equal.
From figure,
PQ = PB + BQ = 10 + 5 = 15 cm.
Hence, the length of PQ = 15 cm.
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