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

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Presentation transcript:

CIRCLES: TANGENTS

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

NO POINTS OF INTERSECTION (DIFFERENT CENTER)

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

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

2 POINTS OF INTERSECTION

COMMON TANGENTS Internal

COMMON TANGENTS External

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!!

a 2 + b 2 = c 2 x = = x 2

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

r = (r + 16) 2 r = 10 r = r r = 32r

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

R S T

A C B

A C E B D P

T S Q P N R