Tangent Lines

Tangent Lines

Let’s explore lines that intersect a circle in exactly 1 point.

• I can use the relationship between tangent lines and radii to calculate angle measures and prove geometric theorems.

• I know that a line tangent to a circle is perpendicular to the radius drawn to the point of tangency.

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​Learning Targets

​Tangent Line

A line is tangent to a circle if the line intersects the circle at exactly one point.

​Point of Tangency:

The point where the tangent line intersects the cirle "C" is the point of tangency.

Fill in the Blanks

Find the measure of $\angle OBA$

Fill in the Blanks

ST is a tangent to ⨀Q.  Find the value of r

Open Ended

Here is a circle centered at O with radius 1 unit. Line AB is tangent to the circle.

Calculate the length of segment.

​Tangent- Chord Theorem

If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one half the measure of its intercepted arc.

Fill in the Blanks

$BC\ is\ \tan gent\ to\ the\ circle.\ Find\ m\angle CBD$

​Theorem

Tangent segments which form a common external point are congruent.

Fill in the Blanks

JK is tangent to circle L at K and JM is tangent to circle L at M. Find the value of x

Fill in the Blanks

JK is tangent to circle L at K and JM is tangent to circle L at M. Find the value of x

Open Ended

Line BC is tangent to the circle.

What is the value of a + c? Explain or show your reasoning.