The triangle DEF which is formed by joining the feet of the altitudes of triangle ABC is called the Pedal Triangle. Answer The Following Questions :
(i) Angle of triangle DEF are
Text Solution
Verified by Experts(ii)(b,c); (iv)(a,b,c,d)
(i)
∠ EDF = 90 – A + 90 – A
= 180 – A
(ii)(b,c) Δ AEF : AF = bcosA, AE = ccosA
∴ cosA = 
⇒ (EF) 2 = (b 2 + c 2 – 2bccosA) cos 2 A
(EF) 2 = a 2 cos 2 A
EF = a.cosA
(iii) Circumraii of the triangle PBC = 
= 
= 
= R
(iv)(a,b,c,d) FE = a cos A = R sin 2A
DE = c cos C = R sin 2C
FD = b cos B = R sin 2B
= 
= 
= 
= 
Area of Δ DEF
= 
FD × DE sin ( π – 2A) = 
b cos B.c cos C.sin 2A
= 
bc cos B.cos C.2 sin A.cos A = 2 
cos A.cos B.cos C
= 2 Δ cos A.cos B. cos C
Area of Δ AEF = 
AE ×AF sin A
= 
(c cos A) (b cos A) sin A = 
cos 2 A = Δ cos 2 A
R DEF = 
= 
= 
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