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Analytical Geometry

New kid on the Block

 Joined: 12 Nov 2008 Post: 26
16 Feb 2009 05:43:53 IST
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to the circle x^2+y^2=25/2 AB is a chord of length 5cm.P is a point such that PA=4cm, PB=3cm find th
Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Analytical Geometry

to the circle x^2+y^2=25/2 AB is a chord of length 5cm.P is a point such that PA=4cm, PB=3cm find the distance between origin and point P.

Blazing goIITian

Joined: 16 Jan 2007
Posts: 1836
16 Feb 2009 06:05:01 IST
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see d fig......

noow using cosine formula in AOP we get

cos(45+theta)=(25/2)^2+9-x^2/15rt2

-1/3=25/2+9-x^2

x=rt131/6

Forum Expert
Joined: 19 Jan 2009
Posts: 304
26 Feb 2009 00:27:55 IST
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AM = MB = 5/2 cm

PA = 4 cm and PB = 3 cm => PAB is a rt. triangle

in tri.OAM, OM2 = OA2 - AM2 => OM2 = 25/2 - 25/4 = 25/4  => OA = 5/2

=> AM = OM => <OAM = 450

using triangle PAQ and PBQ and applying pytha thm we can find the value of x and PQ, where MQ = x

on solving x = 7/10 hence PQ = 13/5

from the triangle PAQ, Tan(450 + @) = PQ/AQ = (13/5) / (16/5) = 13/16  =>  Tan@ = 11/21   => Cos@ = 21/sqrt.310

in tr.OAP,  COS@ = (OA2 + AP2 - OP2) / 2.OA.AP

now OP can easily be calculated

plz ignore the calculation mistake if done anywhere by mistake

but i think the logic is clear to u

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