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 B203cm In the given figure, PQ =8 cm and OP =5cm
OR⊥PQ 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+PR2⇒52=OR2+42 ⇒ OR=3cm In ΔTPO and ΔPRO, ∠TOP=∠ROP [common] and ∠TPO=∠PRO [each 90∘] ∴ΔTPOandΔPROaresimilar [by AAA Similarily] ⇒TPPO=RPRO⇒TP5=43∴TP=203cm