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ICSE Class 9 Answered

ABC is an isosceles triangle inscribed in a circle. If ab=ac=12root5 cm and bc=24cm. Find the radius. (4 marks) 
Asked by Prajvalsaraff | 05 Jan, 2019, 10:55: PM
answered-by-expert Expert Answer
ΔABC is isoceles, AD is perpendicular bisector to BC
AD2 = AB2 - BD2 = (12×12×5) - (12×12) 
Hence AD = r+h = 24 cm .......................(1)
 
OB2 = r² = 12×12 + h² 
Hence  (r² - h² ) = (r+h)(r-h) = 24×(r-h) = 12×12
 
hence we get (r-h) = 6 cm ..........................(2)
 
By solving (1) and (2), we get r = radius of circle = 15 cm
Answered by Thiyagarajan K | 06 Jan, 2019, 11:50: AM

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