Tangent Lines in Circles
Tangent Lines
A tangent line to a circle is a line in the plane of the circle that intersects the circle in exactly one point.
The point where a circle and a tangent intersect is the point of tangency (Point B on the circle to the right).
Theorem
If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency.
Example 1: Finding Angle Measures
ML and MN are tangent to Circle O. Find the value of x.
Step 1
ML and MN are tangent to Circle O. So, they create 90 degree angles at L and N.
Step 2
MNOL now makes a quadrilateral (4 sided figure). A Quadrilateral has 360 degrees.
Step 3
To find the missing angle, add the existing angles and subtract from 360.
Example 2:
A dirt bike chain fits tightly around two gears. The chain and gears form a figure like the one at the right. Find the distance between the centers of the gears.