The circular geometry is really vast. A circle consists of many parts and angles. These parts and angles are mutually supported by certain Theorems, e.g., the Inscribed Angle Theorem, Thales’ Theorem, and Alternate Segment Theorem.
You are watching: An angle whose vertex is the center of a circle
We will go through the inscribed angle theorem, but before that, let’s have a brief overview of circles and their parts.
Circles are all around us in our world. There exists an interesting relationship among the angles of a circle. To recall, a chord of a circle is the straight line that joins two points on a circle’s circumference. Three types of angles are formed inside a circle when two chords meet at a common point known as a vertex. These angles are the central angle, intercepted arc, and the inscribed angle.
For more definitions related to circles, you need to go through the previous articles.
In this article, you will learn:
The inscribed angle and inscribed angle theorem,we will also learn how to prove the inscribed angle theorem.
What is the Inscribed Angle?
An inscribed angle is an angle whose vertex lies on a circle, and its two sides are chords of the same circle.
On the other hand, a central angle is an angle whose vertex lies at the center of a circle, and its two radii are the sides of the angle.
The intercepted arc is an angle formed by the ends of two chords on a circle’s circumference.
Let’s take a look.
For the circle above, XY is the diameter, and O is the circle. The vertex of the angle is at its center.