self Maths Puzzle

Two circles of radius 4cm, and 9cm touch each other externally. A common tangent AB is drawn to these two circles, A and B lie on the two circles respectively. Then the radius of the circle which touches the given circles, and also whose tangent is line AB is(a) 1.32 cm (b) 1.44 cm (c) 1.56 cm (d) 1.68 cm

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self Other Question

If x sin^3 theta +y cos^3 theta+sin theta cos theta and xsin theta +y cos theta, sin theta is not equal to 0,cos theta is not equal to zero,then x^2 + y^2 is a^3 - b^3 - 3ab = 1

Prove that
(a^3 - b^3 + ab) is a perect square.