Latest CAT Aptitude Question SOLUTION: a tangent pr touches a circle at point p and pq is diameter of cir cle =8 pr-=6 cm qr cut the circle at point m then find the ratio of triangle perimeter pmr to pqr

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a tangent pr touches a circle at point p and pq is diameter of cir cle =8 pr-=6 cm qr cut the circle at point m then find the ratio of triangle perimeter pmr to pqr

Asked In CAT shalini mishra (12 years ago)

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Suraj Lal Gupta  (12 years ago)

PR^2 = RM*RQ
=>RM*RQ = 6^2 = 36 ....1.
also,
in right-angled triangle
PR^2 + PQ^2 = QR^2
=> 36 + 64 = QR^2
=>QR = 10 ....2.
using 1. and 2. we get
MR = 3.6
so, QM = QR - MR = 10-3.6 = 6.4
now, since PQ is a diameter
som PMQ is a right-angled triangle right angled at M
so, PM = sqrt(PQ^2 - QM^2) = sqrt(10^2 - 6.4^2) = 4.8
perimeter of PMR = PM + MR + PR = 6+3.6+4.8 = 14.4
perimeter of PQR = PR + QR + PQ = 8 + 6+ 10 = 28
so ratio = 14.4/28 = 18/35

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billa_rana  (12 years ago)

wrong question i guess

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sneha  (12 years ago)

haha elitmus aspirants

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