bisectors of angle A B and C of a triangle ABC int

Question

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.

Yash Mandil · Accepted Answer

there is also a image of this question which I can not insert in answer that’whyI 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/2Similarly, ∠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

9 grade maths> bisectors of angle A B and C of a triangl...

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.

Rahul Jiji George , 10 Years ago

Yash Mandil

LIVE ONLINE CLASSES

In the figure (not to scale) AB = CD, angle DAP = angle DPA and A,B,C,D are concycli. If angle ADC = 80°, then find angle ACD.

9 grade maths

Solve : 2^(x+2)+2^(x-1)=9

9 grade maths

Volume of a Cylinder

9 grade maths

What length of tarpaulin 3m wide will be required to make conical tent of height 8m and base radius 6m ? Assume that the extra length of material that will be required for stitching and wastage in cutting is approximately 20cm ( Use pi= 3.14)

9 grade maths

Find the square of: 2a +b

9 grade maths

9 grade maths> bisectors of angle A B and C of a triangl...

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.

Rahul Jiji George , 10 Years ago

Yash Mandil

LIVE ONLINE CLASSES

Other Related Questions on 9 grade maths

In the figure (not to scale) AB = CD, angle DAP = angle DPA and A,B,C,D are concycli. If angle ADC = 80°, then find angle ACD.

9 grade maths

Solve : 2^(x+2)+2^(x-1)=9

9 grade maths

Volume of a Cylinder

9 grade maths

What length of tarpaulin 3m wide will be required to make conical tent of height 8m and base radius 6m ? Assume that the extra length of material that will be required for stitching and wastage in cutting is approximately 20cm ( Use pi= 3.14)

9 grade maths

Find the square of: 2a +b

9 grade maths