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Theorem of Equal Angles Subtended by Different Chords

in the figure...

Question

in the figure BD is the angle bisector of angle B in triangle ABC, point E is on AB and CE intersects BD at P. Quadrilateral BCDE is ccyclic.If BP=15cm and PE=5 cm and AE/AC=m/n, where m and n are in lowest form then find m+n.

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Q. Suppose ABC is an isosceles triangle with

A B = A C

; BD and CE are bisectors of

∠ B

∠ C

B D = C E

A B C D

, its diagonals

A C

B D

intersect each other at point

O

. The bisector of angle

D A O

B D

M

and the bisector of angle

A B D

A C

N

A M

L

∠ O N L + ∠ O M L = 180^{o}

∠ B A M = ∠ B M A

A L O B i s a c y c l i c q u a d r i l a t e r a l

.

A D

D

B C

be the bisector of

∠ A

Δ A B C

b = A C, c = A B, m = C D

n = B D

A B C

D

E

B C

A C

respectively such that

¯ B D = ¯ 2 D C

and \bar { AE }=\bar { 3EC } Let

p

be the point of intersection of

A D

B E

B P / P E

△

∠ B = ∠ C

, D and E are the points on AB and AC such that BD = CE, prove that DE || BC.

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Theorem of Equal Angles Subtended by Different Chords

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