Question

in triangle abc, bc produced to d. bisectors of angle abc and angle acd meet at point e. if angle bec=25 degree then angle bac is equal to what?​

Answer 1

Answer:

Given- ΔABC has been inscribed in a circle. AE, the bisector of ∠BAC, meets BC at D and the arc BEC at E. ∠ECD=30

o

when EC is joined.

To find out- ∠BAC=? Solution- We join BE. Now, BE, the chord of the given circle, subtends ∠BAE&∠BCE to the circumference of the given circle at A & C respectively. So ∠BAE=∠BCE.......(i) (since angles, subtended by a chord of a circle to the circumference of the same circle at different points, are equal.)

But ∠BAE=∠EAC........(ii) since AE is the bisector of \angle BAC.

∴ From (i) & (ii) ∠BCE=∠BAE=∠EAC=30

o

.

∴∠BAC=∠BAE+∠EAC=30

o

+30

o

=60

o

.

Ans- Option D.