Trigonometry + GeometryDate: 5/5/96 at 12:39:45 From: Anonymous Subject: Trigonometry and Geometry A circle is inscribed in a right angle triangle (90 degrees), and another circle is circumscribed around the triangle. The ratio of the radii of the circles is 13 to 4. What are the other two angles of the triangle? Date: 10/31/96 at 17:13:31 From: Doctor Ceeks Subject: Re: Trigonometry and Geometry Hi, If R is the circumscribed circle radius and r is the inscribed circle radius, and a,b,c are the sides of the triangle, we have these equations: Pythagoras: a^2 + b^2 = c^2 Computation of areas: ab = (a+b+c)r Hypotenuse of right triangle is diameter of circumscribed circle: c = 2R Because angles don't change under dilation, you can assume that r = 4, R = 13. That gives three equations in three unknowns, and you can solve them and ultimately compute arccos(a/c), arccos(b/c) for the answer. -Doctor Ceeks, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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