Given an isosceles triangle with equal side of length b and base angle α < π / 4, then
(i) The circumradius R is given by-
Text Solution
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Ans.
(i)
Sol. AB = AC = b ; ∠ B = ∠ C = α
Since O be the circum centre ∴ OA = OB = R
in isosceles Δ OAB
= 
;
R = 
= 
r = 
= 
= 
OI = | OD + DI | = | OD + r |
α < 
; ∴ A > 
so lies on AU produced.
In Δ ODB, OD 2 = OB 2 – BD 2 = R
2 – (bcos α ) 2 = 
= 
= 
= 
∴ OD = 
∴ OI = 
= 
= 
= 
(ii)
Sol. AB = AC = b ; ∠ B = ∠ C = α
since O be the circum centre ∴ OA = OB = R
in isosceles Δ OAB
= 
;
R = 
= 
r = 
= 
= 
OI = | OD + DI | = | OD + r |
α < 
; ∴ A > 
so lies on AU produced.
In Δ ODB, OD 2 = OB 2 – BD 2 = R
2 – (bcos α ) 2 = 
= 
= 
= 
∴ OD = 
∴ OI = 
= 
= 
= 
(iii)
Sol. AB = AC = b ; ∠ B = ∠ C = α
Since O be the circum centre ∴ OA = OB = R in isosceles Δ OAB
= 
;
R = 
= 
r = 
= 
= 
OI = | OD + DI | = | OD + r |
α < 
; ∴ A > 
so lies on AU produced.
In Δ ODB, OD 2 = OB 2 – BD 2 = R
2 – (bcos α ) 2 = 
= 
= 
= 
∴ OD = 
∴ OI = 
= 
= 
= 
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