A simple geometry-circled question

Geometry Level 2

In the circle below with centre $O$ , the points $A$ , $P$ , $B$ and $C$ are situated on the circle. The measure of $\angle ACB$ is $30^\circ$ .

What are the values of $x$ ( $\angle APB$ ) and $y$ ( $\angle AOB$ ) in degrees in the diagram?

x = 30°

y = 120°

x = 45°

y = 90°

x = 60°

y = 45°

x = 30°

y = 60°

2 solutions

A Former Brilliant Member
May 4, 2020

In a circle, all inscribed angles with the same endpoint/startpoint are equivalent to each other, which shows that

Angle ACB is equivalent to angle $x$ ; which is equivalent to 30°

$x = 30°$

As an angle with the intersection point as the centre of a circle and the end points lying on the circle are twice the angle value of an inscribed angle, we can assure that

Angle $y = 2x = 60°$ [We have proved that $x = 30°$ ]

Therefore, the correct choice for the question is choice 4

Trupal Panchal
May 7, 2020

In a circle, all inscribed angles with the same endpoint/startpoint are equivalent to each other, which shows that

Angle ACB is equivalent to angle xx; which is equivalent to 30°

x = 30°x=30°

As an angle with the intersection point as the centre of a circle and the end points lying on the circle are twice the angle value of an inscribed angle, we can assure that

Angle y = 2x = 60°y=2x=60° [We have proved that x = 30°x=30°]

A simple geometry-circled question

2 solutions

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