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Question

Two circle with centres O and O' touch each other externally at point p and XY is a common tangent to the two circles at P. prove that O,P,O' are collinear.

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Solution

We have

Then,

O and Obe the centre of two circles.

XY be a common tangent.

P is the mid point of OandO.

Construct:-draw OX and OX.

Then,

InΔOPXandOPX

OP=OP(radiusofcircle)

PX=PX(Commonline)

XPO=XPO(Every90o)

Then,

ΔOPXΔOPX

So, OPO are collinear.
1167083_1153325_ans_7e42adb2c6cd420c8c795edda3794207.png

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