Q. 24.2( 11 Votes )

Two circles touch

Answer :

Given X and Y are two circles that touch each other externally at P. AB is the common tangent to the circles X and Y at point A and B respectively.

We have to find APB.

Let CAP = α and CBP = β

CA = CP [The lengths of the tangents from an external point C]

In ΔPAC, CAP = APC = α

Similarly, CB = CP and CPB = PBC = β

We know that sum of interior angles in a triangle is 180°.

Now in ΔAPB,

PAB + PBA + APB = 180°

α + β + (α + β) = 180°

2α + 2β = 180°

α + β = 90°

APB = α + β = 90°

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