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11.1 Tangent Lines

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. M. L.

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11.1 Tangent Lines

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  1. 11.1 Tangent Lines Chapter 11 Circles

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

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

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

  5. ED is tangent to Circle O. Find the value of x. 38 + 90 + x = 180 38° x = 52° O x° E D

  6. C 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. E 26.5 in 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. AD = 27.4 in 26.52 + 6.92 = c2

  7. 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

  8. 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 ?? M 25 N 625 = 625 24 7 Yes, ML is tangent to circle N L

  9. 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.

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

  11. 10 15 8 P = 66 The two segments tangent to a circle from a point outside the circle are ____________! congruent Ex. 3: Find the perimeter of the triangle! P = 10 + 10 + 15 + 15 + 8 + 8

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

  13. Homework: Pg 586-9: # 1 – 22

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