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Tangents. A tangent is a line in the same plane as a circle that intersects the circle in exactly one point, called the point of tangency. A common tangent.

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Presentation on theme: "Tangents. A tangent is a line in the same plane as a circle that intersects the circle in exactly one point, called the point of tangency. A common tangent."— Presentation transcript:

1 Tangents

2 A tangent is a line in the same plane as a circle that intersects the circle in exactly one point, called the point of tangency. A common tangent is a line, ray, or segment that is tangent to two circles in the same plane. In each figure below, in l is a common tangent of circles F and G.

3 Example 1: a) Using the figure below, draw the common tangents. If no common tangent exists, state no common tangent. These circles have no common tangents. Any tangent of the inner circle will intercept the outer circle in two points.

4 Example 1: b) Using the figure below, draw the common tangents. If no common tangent exists, state no common tangent. These circles have 2 common tangents.

5

6 Example 2: Test to see if ΔKLM is a right triangle. ? 20 2 + 21 2 = 29 2 Pythagorean Theorem 841 =841 Simplify.

7 Example 2: Test to see if ΔXYZ is a right triangle. ? 14 2 + 16 2 = 21 2 Pythagorean Theorem 452 ≠441Simplify.

8 Example 3: EW 2 + DW 2 =DE 2 Pythagorean Theorem 24 2 + x 2 =(x + 16) 2 EW = 24, DW = x, and DE = x + 16 576 + x 2 =x 2 + 32x + 256Multiply. 320 =32xSimplify. 10 =xDivide each side by 32.

9 Example 3: JK 2 + KI 2 =IJ 2 Pythagorean Theorem x 2 + 16 2 =(x + 8) 2 JK = x, KI = 16, and JI = x + 8 x 2 + 256 =x 2 + 16x + 64Multiply. 192 =16xSimplify. 12 =xDivide each side by 16.

10

11 Example 4: AC =BCTangents from the same exterior point are congruent. 3x + 2 =4x – 3Substitution 2 =x – 3Subtract 3x from each side. 5 =xAdd 3 to each side.

12 Example 4: MN =MPTangents from the same exterior point are congruent. 5x + 4 =8x – 17Substitution 4 =3x – 17Subtract 3x from each side. 21 = 3xAdd 17 to each side. 7 =xDivide each side by 7.

13 Circumscribed Polygons A polygon is circumscribed about a circle if every side of the polygon is tangent to the circle.

14 Example 5: a) The round cookies are marketed in a triangular package to pique the consumer’s interest. If ∆QRS is circumscribed about T, find the perimeter of ∆QRS.

15 Find the perimeter of ΔQRS.

16 Example 5: b) A bouncy ball is marketed in a triangular package to pique the consumer’s interest. If ∆ABC is circumscribed about G, find the perimeter of ∆ABC.

17 Find the perimeter of ΔQRS.

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