Triangle ABC, with obtuse angle B, is inscribed in a circle. Altitude CH of the triangle is tangent to the circle. If AB=8 and BH=10, find the radius of the circle.
(In reply to
No Subject by jim)
Yes, 14 is the answer.
AB, of length 8, is a chord of the circle. Its perpendicular bisector goes through the center of the circle. Therefore the altitude dropped from C is parallel to that perpendicular bisector, and meets the extended AB at H. If M is the midpoint of AB and O is the center of the circle, OMHC is a rectangle. Since AB is 8, MB is 4; then since BH is 10, MH is 14, as then is OC, the radius of the circle.

Posted by Charlie
on 20050507 19:53:17 