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Olympiad workbookIOQMProperties of Triangles

The centre of the circle passing through the midpoints of the sides of an isosceles triangle A B C lies on the circumcircle of triangle A B C . If the larger angle of triangle A B C is ^0 and the smaller one ^ then what is the value of - ?

Correct answer

90

Step-by-step solution

aligned & A+2 B=180 & A 2 =90-B & 2 x+2 B=180 & x=90-B & x= A 2 & O P B C aligned O and A coincide aligned & ORP = OPR = RAP =60^ & =120^ =30^ & - =90^ aligned By drawing properly we get

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