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Let I be the incetre of ΔABC having inra...

Let I be the incetre of ΔABC having inradius r. Al, BI and Ci intersect incircle at D, E and F respectively. Prove that area of Δ D E F is r 2 2 ( cos . A 2 + cos . B 2 + cos . C 2 ) DeltaDEF " is " (r^(2))/(2) (cos.(A)/(2) + cos.(B)/(2) + cos.(C)/(2))

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