Question

PLEASE ANSWER. ITS URGENT PLEASEE.
In the given figure, angleABC is inscribed in a circle. If
the bisector of angleBAC meets BC at D and the circle
at E such that angleECD = 30°, then angleBAC is
А
30°
D
B
С
E
(1) 30°
(3) 50°
(2) 40°
(4) 60°
PLEASE ANSWER. PLEASEEE​

Answer 1

Answer:

(4)

Step-by-step explanation:

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.