Find the circumradius of a triangle whose sides are 50, 50, and 60. The answer i

Question

Find the circumradius of a triangle whose sides are 50, 50, and 60. The answer is 31.25 [or simply 31;15 if you are working in the base 60 Babylonian way, where recall the expression 9,20,8;30,10,23 means 9(60)^2+20(60)+8+30/60+10/(60)^2+23/(60)^3].

Solve the above problem and clearly explain why the answer is 31.25 (or 31;15). [Hint: Use the fact that the center of a circle lies on the perpendicular bisector of any chord of the circle and note that the sides of the triangle of lengths 50 and 60 are two chords of the circumscribing circle. Similar triangles should come in handy.].

Explanation / Answer

a/sinA=b/sinB=c/sinC=2R [Law of Sines]
a=50
b=50
c=60
cosA=b2+c2-a2/2bc=60/100=3/5

=>sinA=4/5

a/sinA=2R

=>R=a/2sinA=50/2*(4/5)=250/8=31.25

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