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Question

In the given figure, PQ is a chord of length 8 cm of a circle with centre O and radius 5 cm. If the tangents to the circle at the points P and Q intersect at 'T', then the length of PT is


A

20 cm

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B

203cm

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C

40 cm

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D

403cm

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Solution

The correct option is B

203cm


In the given figure,
PQ =8 cm and OP =5cm

ORPQ and so, OR bisects PQ. (The perpendicular line drawn from the center of a circle to the chord bisects the chord)
PR=RQ=4cm
In ΔPOR,
OP2=OR2+PR252=OR2+42
OR=3cm
In ΔTPO and ΔPRO,
TOP=ROP [common]
and TPO=PRO [each 90]
ΔTPO and ΔPRO are similar [by AAA Similarily]
TPPO=RPROTP5=43TP=203cm


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