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Question

In the given figure, A rigtht angled ABC at B is circumscribing a circle. If AP = 8 cm and BQ = 4 cm, then the length of AC = .

A
24 cm
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B
16 cm
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C
20 cm
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Solution

The correct option is C 20 cm
Let us assume CR = x cm
By Theorem- Tangents from an external point to a circle are equal in lengths.
AR=AP=8 cm,
BP=BQ=4 cm, and
CQ=CR=x cm

Applying pythagoras theorem, we get,
AB2+BC2=AC2
(AP+PB)2+(BQ+CQ)2=(AR+CR)2
(8+4)2+(4+x)2=(8+x)2
122+(4+x)2=(8+x)2
144+16+x2+8x=64+x2+16x
8x=144+1664
x=968=12 cm

CR=x=12 cm and AC=AR+CR
AC=8+12=20 cm

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