Question

if two circles touch each other externally prove that center and point of contact and collinear​

Answer 1

Answer:

Two circles with centres A and B touch each other at P externally.

To prove: A,B and P are collinear.

Construction: Draw the common tangent at P. Join AP and BP.

Proof: ∠APQ=90

o

.....(i)

(Radius is perpendicular to the tangent)

∠BPQ=90

o

.....(ii)

(radius is perpendicular to the tangent)

Adding (i) and (ii), we get

∠APQ+∠BPQ=90

o

+90

o

⇒∠APB=180

o

⇒ APB is a straight line

∴ A,B and P are collinear.

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