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# In the diagram, 0 is the centre of the circle. Find the value x.

### Question

In the diagram, 0 is the centre of the circle. Find the value x.

### Options

A) 34

B) 29

C) 17

D) 14

The correct answer is D.

### Explanation:

POQ in a straight line
Hence, < POQ + < QOR = 180$$^{\circ}$$
56$$^{\circ}$$ + < QOR = 180$$^{\circ}$$
< QOR = 180$$^{\circ}$$- 56$$^{\circ}$$
= 124$$^{\circ}$$
Now, in $$\bigtriangleup$$ QOR OR = OQ = Radius
< ORQ = < OQR = 2x (Base angles of an Isosceles $$\bigtriangleup$$)
2x + 124 + 2x = 180$$^{\circ}$$
4x + 124 = 180
4x = 180 - 124
4x = 56
x = $$\frac{56}{4}$$
x = 14$$^{\circ}$$

## Dicussion (1)

• POQ in a straight line
Hence, < POQ + < QOR = 180$$^{\circ}$$
56$$^{\circ}$$ + < QOR = 180$$^{\circ}$$
< QOR = 180$$^{\circ}$$- 56$$^{\circ}$$
= 124$$^{\circ}$$
Now, in $$\bigtriangleup$$ QOR OR = OQ = Radius
< ORQ = < OQR = 2x (Base angles of an Isosceles $$\bigtriangleup$$)
2x + 124 + 2x = 180$$^{\circ}$$
4x + 124 = 180
4x = 180 - 124
4x = 56
x = $$\frac{56}{4}$$
x = 14$$^{\circ}$$