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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 find the length of TP.

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Solution

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

ORPQ and so, OR bisects PQ. [ Perpendicular drawn from the center to the chord bisects the chord]
PR=RQ=4 cm

In ΔPOR,
OP2=OR2+PR252=OR2+42
OR = 3 cm
In ΔTPO and ΔPRO,
TOP=ROP [common]
and TPO=PRO [each 90]
ΔTPO and ΔPRO are similar. [by AAA Similarity]
TPPO=RPROTP5=43TP=203 cm


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