Section 9.2 TANGENTS

Drawing Activity It is 90o Draw a circle. Plot a point on the circle. Draw a radius from the center to the point on the circle. Draw a segment tangent to the circle through that point. What do you notice about the angle formed by the radius and the tangent segment? It is 90o

If OR = 12 and OT = 16, then RT = ? If m∠OTR = 45o, and RT = 4, then OT = ? 20 Hint: Use Pythagorean Theorem… Even better see if it’s a Pythagorean Triple! R is the center of the circle. It’s a Special Right Triangle … 45-45-90. It is a 3, 4, 5 triangle (multiple of it) so x = 20 because each side increased by 4x. 12 4 x 16 x 45o

Activity #2 Draw another circle. Plot a point outside of the circle. Draw two tangents from the point to the circle. (only hit the circle once from each tangent) What do you notice about the lengths of the two tangents? The lengths are equal.

The following shows tangents and circles. Find the missing values. y = 7.94 x = 7.94 z = 7.94

Tangent LINES Circles can have common tangent LINES. Common internal tangent line: intersects the segment joining the centers. Common external tangent line does not intersect the segment joining the centers.

Tangent CIRCLES Tangent circles are coplanar circles that are tangent to the same line at the same point. Internally tangent Externally tangent

How many common external tangents can be drawn? 1) 2

How many common internal tangents can be drawn? 2) 1

There is a difference between TANGENT LINES and TANGENT CIRCLES! Remember! There is a difference between TANGENT LINES and TANGENT CIRCLES!

PRACTICE Page 335 Written Exercises #1 - 6, 8, 16, 17