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Let D be an interior point of the side BC of a triangle ABC . Let I ₁ and I ₂ be the incentres of triangles A B D and A C D respectively. Let A I₁ and A I₂ meet B C in E and F respectively. If B I₁ E=60^ . What is the measure of C I₂ F in degrees?

Correct answer

30

Step-by-step solution

aligned & BAD =120^ - B & CAD = A - (120^ - B ) & = A + B -120^ & FAC = A + B 2 -60^ 90^ - C 2 -60^ 30^ - C 2 & AFC =180^ - ( C +30^ - C 2 ) & =150- C / 2 & Cl ₂ ~F =180^ m - (150^ - C 2 + C 2 )=30^ aligned

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