Published by:
CGP EDU Academic Team
Published on: August 13, 2026
The internal bisectors of angles A, B, C of triangle ABC meet the circumcircle at D, E, F respectively. Let R be the circumradius and s the semi-perimeter of triangle ABC.
(i) EF =
A
Rs 
B
2 Rs 
C
D
(ii) The area Δ DEF = 
(iii)The ratio of the inradius to the circumradius of Δ DEF = 
Text Solution
Verified by ExpertsThe correct answer is:
D
Ans.
(i)
Sol. D = 
= 
, E = 
, F = 
EF = 2R and sin D = 2R cos 
(ii)
Sol. Δ DEF = 2R 2 sinD sinE sinF
= 2R 2 cos 
cos 
cos 
= 
(iii)
Sol. 
= 
= 
= 
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