Question

X Q24.
In the given figure, O is the center of the circle. If ZBAC-40°. Find ZBOC and BDC.​

Answer 1

Step-by-step explanation:

In the given figure O is the centre of the circle, ∠BAD = 75° and chord BC = chord CD Find : (i) ∠BOC (ii) ∠OBD (iii) ∠BCD.Read more on Sarthaks.com - https://www.sarthaks.com/260828/in-the-given-figure-o-is-the-centre-of-the-circle-bad-75-and-chord-bc-chord-cd-find

so,

(i) Given, ∠BAD = 75° and chord BC = chord CD ∠BOD = 2. ∠BAD (Angle at the centre is twice the angle at the remaining part of the circle) Read more on Sarthaks.com - https://www.sarthaks.com/260828/in-the-given-figure-o-is-the-centre-of-the-circle-bad-75-and-chord-bc-chord-cd-find

Answer 2

Answer:

Incentre is defined as Intersection of angle bisectors of vertices of a triangle.

=> AF, BE, CD are angle bisectors.

=> ∠BAF=∠FAC=20

=>Let ∠ABE=∠FBE=x

=>Let ∠BCD=∠ACD=y

Now, using the exterior angle property of a triangle, ∠FOC=20+y and ∠BOF=20+x

in triangle BOC, using the property that sum of all angles of triangle is 180, we can say that

20+y+20+x+x+y=180

=> x+y=70

∠BOC=20+y+20+x=110