ABC is an isosceles triangle inscribed in a circle if ab = AC = 6root 5 cm and BC is equals to 12 cm find the radius of the circle.
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AABC is isoceles, AD is perpendicular bisector to BC
AD² = AB² - BD² = (12×12×5) - (12×12)
Hence AD = r+h = 24 cm ....
OB2 = r2 = 12×12 + h2
Hence (r2 - h² ) = (r+h)(r-h) = 24x(r-h) = 12x12
hence we get (r-h) = 6 cm
(2)
By solving (1) and (2), we get r = radius of circle = 15 cm
... (1)
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