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CIRCLES: TANGENTS. TWO CIRCLES CAN INTERSECT… in two points one point or no points.

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Presentation on theme: "CIRCLES: TANGENTS. TWO CIRCLES CAN INTERSECT… in two points one point or no points."— Presentation transcript:

1 CIRCLES: TANGENTS

2 TWO CIRCLES CAN INTERSECT… in two points one point or no points

3 NO POINTS OF INTERSECTION (DIFFERENT CENTER)

4 NO POINTS OF INTERSECTION (SAME CENTER) Same center but different radii

5 1 POINT OF INTERSECTION (TANGENT CIRCLES) Internally Tangent Externally Tangent

6 2 POINTS OF INTERSECTION

7 COMMON TANGENTS Internal

8 COMMON TANGENTS External

9 If a line (segment or ray) is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency. Point of Tangency More Pythagorean Theorem type problems! Yeah!!

10 a 2 + b 2 = c 2 x = 15 9 2 + 12 2 = x 2

11 a 2 + b 2 = c 2 RQ = 16 12 2 + (QR) 2 = (8+12) 2 12 2 + (QR) 2 = 20 2

12 r 2 + 24 2 = (r + 16) 2 r = 10 r 2 + 576 = r 2 + 32r + 256 320 = 32r

13 R S T If two segments from the same exterior point are tangent to a circle, then they are congruent. Party hat problems!

14 R S T

15 A C B

16 A C E B D P

17 T S Q P N R

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