+537 Two perpendicular diameters AB and CD of a circle intersect at the center O. A second circle is tangent to the first circle at B, and intersects AO and CO at P and Q, respectively. If AP = 10 and CQ = 7, then find the radius of the larger circle.
+129852 See the following image :
Let the radius of the large circle = R
Due to symmetry, QF = EF = R - 7
And PF = R - 10
And FB = R
And by the intersecting chord theorem in the smaller circle
(QF)(EF) = (PF)(FB)
(R - 7) (R - 7) =(R- 10)(R)
(R - 7) (R -7) = R^2 - 10R
R^2 - 14R + 49 = R^2 - 10r rearrange as
49 = 4R
R = 49/4 = 12.25 = the radius of the larger circle
