circle qs | CAT4MBA

circle qs

Submitted by Incognito on Thu, 2008-09-04 07:24

Geometry

There are three circles with centers at P, Q and R such that they form a right angle triangle(right angle at R) and no two circles intersect each other. AB is a tangent to all the three circles touching A, C and B on the circles with center P, R and Q respectively. l(AB) is 7 cm and l(AC) is 3 cm. Find the radius of the circle with center R if radius of circles with centers P and Q are 2cm and 1cm respectively.
a. sqrt2 cm
b. 1 cm
c. 2 cm
d. 2.5 cm

Posted on: Fri, 2008-09-05 20:05 #1

yadavmillion's picture

Joined: 2008-07-19

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MY ANS IS

MY ANS IS SQRT2 cm

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Posted on: Mon, 2008-09-08 14:50 #2

jigar_er_civil's picture

Joined: 2007-09-03

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Let AB intersects PR and

Let AB intersects PR and QR at M and n respectively ....

considering , CN =y1 ,CM =y2 and CR = r ,

now triangles APM, CRM,CRN & BNQ are similar triangles...

from triangles APM, CRM: r/y2 =2/(3-y2) =(r+2)/3

similarly from triangles CRN & BNQ : r/y1=1/(4-y1) =(r+1)/4

again from trianglesCRM,CRN : r/y1= y2/r

or, (r+2)/3 =4/(r+1)

or, r^2+3r+2=12

or, r^2+3r-10=0

or r =2 cm

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