11.1 Tangent Lines Chapter 11 Circles.

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Presentation transcript:

11.1 Tangent Lines Chapter 11 Circles

Tangent to a circle: a line that touches the circle at one point Point of tangency: the point where the line and circle touch

Theorem 11-1: If a line is tangent to a circle, then it is perpendicular to the radius.

Lines ML and MN are tangents to Circle O. Find the value of x. What are the measures of <OLM and <ONM? 90° 117° O 117 + 90 + 90 + x = 360 N x = 63°

ED is tangent to Circle O. Find the value of x. 38° x = 52° O x° E D

A dirt bike chain fits tightly around two gears A dirt bike chain fits tightly around two gears. The chain and gears form a figure like the one below. Find the distance between the centers of the gears. C 26.5 in E 9.3 in B D 2.4 in A ABCE is a rectangle and AED is a right triangle. AE is 26.5 ED is 9.3 – 2.4 = 6.9 Use Pythagorean Theorem to solve for AD. 26.52 + 6.92 = c2 AD = 27.4 in

A chain fits tightly around two circular pulleys A chain fits tightly around two circular pulleys. Find the distance between the centers of the pulleys. 35in 14in 8in 352 + 62 = c2 c = 35.5in

If a line is perpendicular to the radius at its endpoint on the circle, then the line is tangent to the circle. Is ML tangent to Circle N at L? 72 + 242 = 252 ?? 49 + 576 = 625 ?? 25 M N 625 = 625 24 7 Yes, ML is tangent to circle N L

If all the vertices of a triangle are on a circle, the triangle is inscribed in the circle When a circle is inscribed in a triangle, the triangle is circumscribed about the circle.

The two segments tangent to a circle from a point outside the circle are ____________!

Ex. 3: Find the perimeter of the triangle! The two segments tangent to a circle from a point outside the circle are ____________! congruent Ex. 3: Find the perimeter of the triangle! 8 10 15 P = 10 + 10 + 15 + 15 + 8 + 8 P = 66

Circle O is inscribed in PQR. PQR has a perimeter of 88cm. Find QY. 15 + 15 + 17 + 17 + x + x = 88 x 64 + 2x = 88 x Y 2x = 24 X 17cm O x = 12 QY = 12 15cm P R Z 15cm 17cm

Homework: Pg 586-9: # 1 – 22