Q3 of 100 Page 17

In Fig. 16.122, O is the centre of the circle. Find ∠BAC.

We have,

∠AOB = 80^o

∠AOC = 110^o

∠AOB + ∠AOC + ∠BOC = 360^o (Complete angle)

80^o + 110^o + ∠BOC = 360^o

∠BOC = 170^o

By degree measure theorem,

∠BOC = 2 ∠BAC

170^o = 2 ∠BAC

∠BAC = 85^o

In Fig. 16.120, O is the centre of the circle. If ∠APB=50°, find ∠AOB and ∠OAB.

In Fig. 16.121, it is given that O is the centre of the circle and ∠AOC=150°. Find ∠ABC.

If O is the centre of the circle, find the value of x in each of the following figures :

O is the circumcentre of the triangle ANC and OD is perpendicular on BC. Prove that ∠BOD= ∠A