bisectors of angle A B and C of a triangle ABC intersect its circumcircle at D , E and F respectively . Prove that the angles of the triangle are 90 -1/2 A , 90 – ½ B and 90 -1/2 C.

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Yash Mandil · Answer

there is also a image of this question which I can not insert in answer that’why I have asked the same question with image kindly refer to that question for image It is given that BE is the bisector of ∠B .: ∠ABE = ∠B/2 However, ∠ADE = ∠ABE (Angles in the same segment for chord AE) ∠ADE = ∠B/2 Similarly, ∠ACF = ∠ADF = ∠C/2 (Angle in the same segment for chord AF) ∠D = ∠ADE + ∠ADF ∠D = ∠B/2 + ∠C/2 = ½ ( ∠B + ∠C ) = ½ ( 180 – ∠A ) {since ∠A + ∠B + ∠C =180 ; angle sum property } = 90 – ∠A/2 Similarly, it can be proved that ∠E = 90 – ∠B/2 & ∠F = 90 – ∠C/2

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bisectors of angle A B and C of a triangle ABC intersect its circumcircle at D , E and F respectively . Prove that the angles of the triangle are 90 -1/2 A , 90 – ½ B and 90 -1/2 C.

bisectors of angle A B and C of a triangle ABC intersect its circumcircle at D , E and F respectively . Prove that the angles of the triangle are 90 -1/2 A , 90 – ½ B and 90 -1/2 C.

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