10 1 Tangents in Circles A tangent to

10. 1 Tangents in Circles A tangent to a circle is a segment, line, or ray that intersects the circle exactly once at its point of tangency.

Tangent Line to Circle Theorem In a plane, a line is tangent to a circle if and only if the line is perpendicular to a radius of the circle at its endpoint on the circle. Note: this is a biconditional statement. It works both ways!

If the radius of the circle measures 5” and m<COB = 60, what is the length of BC? HINT: Use special right triangle rules.

How long is the radius of this circle if the segment that is 16 units is a tangent segment? Use Pythagorean Theorem and FOIL 162 + x 2 = (8 + x)2 256 + x 2 = 64 + 16 x + x 2 256 = 64 + 16 x 196 = 16 x x = 12

IS PT a tangent segment when TO = 24, PT = 44, and OP = 51? Use the Pythagorean Theorem. • 242 + 442 = 512 • 576 + 1936 = 2601 • 2512 = 2601 FALSE • It does not work. <T must not be a right angle, so the segment is not a tangent.

Ice Cream Cone Theorem What is true about any length from the tip of the cone to the base of the cone? What do these lengths represent with respect to the “circle” (ice cream scoop)?

Ice Cream Cone Theorem: Two tangent segments drawn from a common external point are congruent.

Find the perimeter of the triangle. HINT: think of it as one scoop and three cones!

Find the perimeter of the triangle. 10 + 7 + 19 = 72 cm

How could we prove the triangles below congruent? Since the triangles are congruent, the angles at point C are also congruent.

Theorem: When two tangent segments are drawn to a circle from a common exterior point, the angle they form is bisected by the segment joining the angle’s vertex to the center of the circle.

Homework: send it to me by Tuesday, 4/14 • 1. Fill in vocabulary on circles vocabulary sheet • 2. Do from your book pages 534 -535 (1 -10, 21, 23, 30, 33 -37) • 3. Study Island Math Challenge must be submitted by Thursday, 4/16.