Understanding Tangent Lines and Circles | Exploring Congruency Between Circumscribed and Central Angles

if two segments or lines are tangent to a circle, then the circumscribed angle and the central angle that intercept the arc formed by the points of tangency are _____________.

If two segments or lines are tangent to a circle, then the circumscribed angle and the central angle that intercept the arc formed by the points of tangency are congruent

If two segments or lines are tangent to a circle, then the circumscribed angle and the central angle that intercept the arc formed by the points of tangency are congruent.

To understand this, let’s break it down:
– Tangent: A tangent is a line or a line segment that touches a circle at exactly one point.
– Circle: A circle is a closed curve consisting of all points in a plane that are a fixed distance (radius) away from a fixed point (center).
– Circumscribed angle: The circumscribed angle is the angle formed by two intersecting lines or segments outside the circle, with each line or segment being tangent to the circle at a different point. This angle opens up outside the circle.
– Central angle: The central angle is the angle formed by two radii or chords of a circle that have their endpoints at the center of the circle. This angle is formed inside the circle.

Now, when two segments or lines are tangent to a circle, they intersect the circle at two points of tangency. These points of tangency divide the circle’s circumference into two arcs.

The circumscribed angle is formed outside the circle by the two lines or segments that are tangent to the circle. This angle intercepts the arc of the circle between the points of tangency.

The central angle, on the other hand, is formed at the center of the circle and intercepts the same arc as the circumscribed angle.

Since both the circumscribed angle and the central angle intercept the same arc, they are said to be congruent or equal in measure.

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