An angle whose vertex lies outside of the circle, but whose sides touch the circle is a
The Correct answer and Explanation is:
The correct term for an angle whose vertex lies outside of a circle, with its sides (or rays) touching the circle, is called an external angle or more specifically, a tangent angle.
Explanation
In geometry, angles can be classified based on their position relative to circles. An external angle, in this context, is formed by two rays or lines that originate from a point outside of the circle and intersect the circle at exactly one point each. These points of intersection are known as the points of tangency.
To understand this concept better, let’s consider a circle with center ( O ). If we have a point ( A ) located outside the circle, we can draw two lines, ( AB ) and ( AC ), such that both lines touch the circle at points ( B ) and ( C ), respectively. The angle ( \angle BAC ) is then the external angle.
The sides of the angle (the rays ( AB ) and ( AC )) are called tangent lines, as they only touch the circle at one point and do not cross into the interior of the circle. The property of tangent lines is that they are perpendicular to the radius drawn to the point of tangency. Thus, if you draw the radius ( OB ) to point ( B ) and radius ( OC ) to point ( C ), both ( OB ) and ( OC ) would form right angles with lines ( AB ) and ( AC ) at points ( B ) and ( C ), respectively.
This type of angle is important in various geometric applications, including construction, architecture, and even in analyzing trajectories in physics. It is also foundational for understanding the properties of circles and tangents in more advanced topics, such as calculus and trigonometry. Overall, recognizing external angles is crucial for solving problems involving circles and their relationships with lines.