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Question

Circle C1 has radius 2 and circle C2 has radius 3, and the distance between the centers of C1 and C2 is 7. If two lines, one tangent to both circles and other passing through the center of both circles, intersect at point P which lies between centers of C1 and C2, the the distance between P and the center of C1

A
94 units
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B
73 units
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C
`83 units
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D
145 units
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Solution

The correct option is D 145 units
REF.Image.
Given : C1M=2cm and NC2=3cm
C1AB=C2BA=90
And C1C2=7cm
To Find :C1P
C1C2=C1M+MN+NC2
MN=2cm
Let MP be x cm, so NP = 2-x
In C1AP and C2BP
C1AP=C2BP=90 [Given]
C1PA=C2PB [vertically opposite angles]
C1APC2BP [by AA similarly]
C1AC2B=APBP=C1PC2P
23=2+x5x
102x=6+3x
5x=4x=45
C1P=C1M+NP
=2+45=145cm Ans

1180373_1166495_ans_7174b5808d2e4ed4abcaaa7acdd7b2f6.jpg

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