Section 9.1Section 9.1Basic terms of Basic terms of Circles

What is a circle?What is a circle?CircleCircle: set of points equidistant from the : set of points equidistant from the

centercenterRadiusRadius: segment from the center to a point : segment from the center to a point

on a circleon a circle

ChordChord: segment with endpoints on a circle: segment with endpoints on a circle

SecantSecant: line that contains a chord: line that contains a chord

DiameterDiameter: a chord that contains the center : a chord that contains the center

of the circleof the circle

TANGENTTANGENTTangentTangent: a line that intersects the circle in : a line that intersects the circle in

exactly one pointexactly one point

Point of tangencyPoint of tangency: the point where the : the point where the tangent line intersects the circletangent line intersects the circle

Tangent Line

Point of Tang.

SpheresSpheresSphereSphere: set of all points in space at : set of all points in space at

the same distance from the centerthe same distance from the center

Congruent CirclesCongruent Circles

(or spheres) are circles (or spheres) that (or spheres) are circles (or spheres) that have congruent radiihave congruent radii

ConcentricConcentricConcentric circlesConcentric circles are circles that lie in the are circles that lie in the

same plane and have the same center. same plane and have the same center.

Concentric spheresConcentric spheres are spheres that have are spheres that have the same centerthe same center

Inscribed vs. CircumscribedInscribed vs. Circumscribed

InscribedInscribed in a circle means on the in a circle means on the insideinside of the circle.of the circle.Try to inscribe a triangle into a circle.Try to inscribe a triangle into a circle.

CircumscribedCircumscribed about a square means a about a square means a circle drawn around a square.circle drawn around a square.Try to circumscribe a rectangle about a Try to circumscribe a rectangle about a

circle.circle.

Inscribed vs. CircumscribedInscribed vs. Circumscribed

Which shape(s) are Which shape(s) are inscribed?inscribed?

Which shape(s) are Which shape(s) are circumscribed?circumscribed?

The square is inscribed in the circle.

The circle is inscribed in the triangle.

The triangle is circumscribed about the circle but NOT the square. (It must hit the endpoints on the square and it doesn’t.)

Copy the following Copy the following diagram.diagram.

1)1) Name three Name three radiiradii

2)2) Name a Name a diameterdiameter

3)3) Why is segment Why is segment TKTK not a chord? not a chord?

4)4) Name a tangent to circle Name a tangent to circle OO..

5)5) What name is given to point What name is given to point LL..

6)6) Consider segment Consider segment RSRS to line to line RSRS. . Which is a chord and which is a Which is a chord and which is a secant?secant?

, , OR OL OT

RLBoth endpoints aren’t ON the circleHL

Point of Tangency

Segment RS is a chord because it has endpoints.

S

O

E

HL

R

T

K

Practice ProblemsPractice Problems

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