Question

In the figure o is the centre of the circle and the length of the arc abc is is twice the length of arc bc if angle aob equals to 104 find by giving reasons. 1.angleboc 2.angleoac 3.anglebac​

Answer 1

∠BOC = 104° , ∠OAC  = 14° ∠BAC = 52°

Step-by-step explanation:

o is the centre of the circle

length of the arc abc is is twice the length of arc bc

arc abc = arc ab + arc bc

2 arc bc = arc ab + arc bc

=> arc ab = arc bc

=> ∠AOB = ∠BOC

∠AOB  = 104°

=> ∠BOC = 104°

∠AOC = 360° - 104° - 104° = 152°

in ΔAOC

∠OAC = ∠OCA  as OA = OC  radius

∠AOC + ∠OAC + ∠OCA =  180°

=> 152° + ∠OAC + ∠OCA =  180°

=> 2 ∠OAC  = 28°

=> ∠OAC  = 14°

∠BAC = (1/2)∠BOC

=> ∠BAC = (1/2)104° = 52°

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