Question

8. Two circles touch each other externally. Prove that the lengths of the tangent drawn to the two
circles from any point on the common tangent lie at the point of contact of two circles are equal.​

Answer 1

Step-by-step explanation:

Given Two circles with centre O and O' touch each other externally and let the point where they touch each other be M.

PM is the common tangent.Let a point P on the common tangent from where tangents PA and PB are drawn to the circles having centres O and O' respectively.

To prove PA = PB

Now as we know that tangents drawn from an external point to a circle are equal in lengthHence consider the circle having centre O P is an external point and let tangents drawn from the point P are PA and PM∴PA = PM ..........(1)Now consider the circle having centre O' P is an external point and let tangents drawn from the point P are PB and PM∴PB=PM........(2)Hence from (1) and (2) we can say thatPA=PB∴Lengths of the tangents drawn to the circle from any point on the common tangent are equal....

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