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CBSE Class 10 Answered

An isosceles triangle ABC is inscribed in a circle. If AB AC 13 cm and BC= 10 cm, find the radius of circle.
Asked by latayadav23 | 14 Oct, 2023, 12:49: PM
answered-by-expert Expert Answer
Figure shows isoceless Δ ABC inscribed inside circle. Perpendicular bisector AD passes through centre O of circle.
 
begin mathsize 14px style A D space equals space square root of A B squared minus B D squared end root space equals space square root of 13 squared minus 5 squared end root space c m space space equals space 12 space c m end style
 
Let OD = h ;  Hence AO = ( 12-h) cm
 
BO = AO = ( 12- h ) cm  [ begin mathsize 14px style because end style OB and Oa are radius of circle )
 
begin mathsize 14px style B O squared space equals space B D squared plus O D squared end style
begin mathsize 14px style left parenthesis 12 minus h right parenthesis squared space equals space 5 squared plus h squared end style
begin mathsize 14px style 144 space minus space 24 h space plus space h squared space equals space 25 space plus space h squared end style
begin mathsize 14px style 24 h space equals space 144 space minus space 25 space equals space 119 end style
h = 4.96 cm
 
Radius = ( 12 - 4.96 ) cm ≈ 7 cm
Answered by Thiyagarajan K | 14 Oct, 2023, 02:20: PM
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