Monday, May 28, 2012

Right Triangle and Square on Hypetenuse

Let ABC be a right triangle with right angle at B. Let AC DE be a square drawn exterior to triangle ABC. If M is the center of this square, find the measure of ∠ MBC.
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Note that triangle MCA is a right isosceles triangle with ∠AMC = 90° and ∠MAC = 45°. Since ∠ABC = 90°, there is a circle k with diameter AC which also passes through points B and C. Chord CM of circle k subtend angles MAC and MBC on the same segment . Hence ∠MBC = ∠MAC = 45°

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