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Inscribed Triangle (Posted on 2005-05-07) Difficulty: 2 of 5
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.

See The Solution Submitted by Jer    
Rating: 1.0000 (1 votes)

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Solution re: No Subject -- yes | Comment 2 of 4 |
(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 2005-05-07 19:53:17
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