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Question

There are two circles each with radius 5 cm. The length of tangent AB is 26 cm. Find the length of tangent CD.


A

15 cm

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B

21 cm

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C

24 cm

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D

16 cm

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Solution

The correct option is C

24 cm



From the figure shown above,
AB = PO = 26 cm

Consider triangle CQP and DQO
∠ CQP = ∠ DQO (Vertically opposite angles)
∠ PCQ = ∠ODQ = 90∘ (Line joining the center to the tangent at the point of contact of the circle)
PC = OD (radius is equal)
therefore the two triangles are congruent using AAS postulate

PQ=QO=262=13 cm

Similarly CQ = QD

Consider triangle PCQ,
Applying Pythagoras Theorem, we get,

CQ2+CP2=PQ2

CQ2+52=132

CQ2 = 13252=144

CQ = 12 cm

Therefore, CD = 2CQ = 24 cm


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