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in a ∆ABC ,the line segments AD,BE and CF are three altitudes.if R is the circumradius of the ∆ABC ,a side of the ∆DEF will be (A) Rsin 2A (B) c cosB (C) a sin A (D) b cosB it has more than one option correct

 
in a ∆ABC ,the line segments  AD,BE and CF are three altitudes.if R is the circumradius of the ∆ABC ,a side of the ∆DEF will be 
(A) Rsin 2A   (B) c cosB   (C) a sin A (D) b cosB
 
it has more than one option correct

Grade:Select Grade

1 Answers

mycroft holmes
272 Points
7 years ago
Consider the feet D, E, F from the Orthocentre H on AB, BC and AC respectively.
 
In triangle DBE, we have BD = a cos B and BE = c cos B (from rt angled triangles BDC and AEB resp.)
 
Now use cosine rule and you will get DE = b cos B = 2R sin B cosB = R sin 2B
 
So options (A) and (D) will be correct

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