Angle inside a circle

Geometry Level 1

$XY$ is a tanget at circle $O$ at point $C$ , find $\theta$ in degrees.

Clarification: Point $O$ is the center of the circle.

The answer is 240.

1 solution

A Former Brilliant Member
Apr 21, 2017

A tangent to a circle is perpendicular to the radius at the point of contact. Therefore, $\angle OCY=90^\circ$ . Then $\angle OCB=90-60=30^\circ$ . Since triangle $OCB$ is isosceles, $\angle OBC=\angle OCB=30^\circ$ . It follows that $\angle COB=180-2(30)=120^\circ$ . Finally $\theta=360-120=240^\circ$ .

I think the problem would benefit from a picture which would not suggest that it is an equilateral triangle.

Marta Reece - 4 years, 1 month ago

Angle inside a circle

The answer is 240.

1 solution

0 pending reports