smc

Question

In the adjoining figure TP and T'Q are parallel tangents to a circle of radius r, with T and T' the points of tangency. PT''Q is a third tangent with T''' as a point of tangency. If TP=4 and T'Q=9 then r is FIGURE

Accepted Answer

FIGURE Drop the perpendicular from P to T'Q and let the foot be R. Note that PTT'R is a rectangle. Also, from Two Tangents, PT''=4 and QT''=9, so PQ=13. Therefore, from the Pythagorean Theorem on PRQ, PR=13^2-5^2=12. We now see that r=PR2=6, 6.