Question

Question 6.
In the following figure, O is the centre of the circle, AE is the angle bisector of ZA and
ZBCO= 30°. Find the value of x and y.
30°
Answer:
Source
E​

Answer 1

Given : O is the centre of the circle, AE is the angle bisector of ∠A

To Find:   value of x and y.

Solution:

∠BCO = 30°

∠OBC = 30°   as OB = OC  ( radius)

=> ∠BOC = 180° - 30° - 30° = 120°

=> ∠BAC = (1/2)∠BOC = 60°

AE is the angle bisector of ∠A

=> x = 60°/2 = 30°  

∠ABD = (1/2)∠AOD = 45°

∠ABD + y + 90° + x = 180°   ( sum of angles of triangle)

=> 45° + y + 90° + 30°  = 180°

=> y = 15°

x =  30°  

y = 15°

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