Download presentation

Presentation is loading. Please wait.

Published byMeryl Catherine Glenn Modified over 7 years ago

1
Lesson 10.1 Circles

2
Definition: The set of all points in a plane that are a given distance from a given point in the plane. The given point is the CENTER of the circle. A segment that joins the center to a point on the circle is called a radius. Two circles are congruent if they have congruent radii.

3
Concentric Circles: Two or more coplanar circles with the same center.

4
A point is inside (in the interior of) a circle if its distance from the center is less than the radius. interior O A Point O and A are in the interior of Circle O.

5
A point is outside (in the exterior of) a circle if its distance from the center is greater than the radius. A W Point W is in the exterior of Circle A. A point is on a circle if its distance from the center is equal to the radius. S Point S is on Circle A.

6
Chords and Diameters: Points on a circle can be connected by segments called chords. A chord of a circle is a segment joining any two points on the circle. A diameter of a circle is a chord that passes through the center of the circle. The longest chord of a circle is the diameter. chord diameter

7
Formulas to know! Circumference: C = 2 π r or C = π d Area: A = π r 2 Area: A = π r 2

8
Radius-Chord Relationships OP is the distance from O to chord AB. The distance from the center of a circle to a chord is the measure of the perpendicular segment from the center to the chord.

9
Theorem 74 If a radius is perpendicular to a chord, then it bisects the chord.

10
Theorem 75 If a radius of a circle bisects a chord that is not a diameter, then it is perpendicular to that chord.

11
Theorem 76 The perpendicular bisector of a chord passes through the center of the circle.

12
1. Circle Q, PR ST 2.PR bisects ST. 3.PR is bisector of ST. 4.PS PT 1.Given 2.If a radius is to a chord, it bisects the chord. (QR is part of a radius.) 3.Combination of steps 1 & 2. 4.If a point is on the bisector of a segment, it is equidistant from the endpoints.

13
The radius of Circle O is 13 mm. The length of chord PQ is 10 mm. Find the distance from chord PQ to center, O. 1.Draw OR perpendicular to PQ. 2.Draw radius OP to complete a right Δ. 3.Since a radius perpendicular to a chord bisects the chord, PR = ½ PQ = ½ (10) = 5. 4.By the Pythagorean Theorem, x 2 + 5 2 = 13 2 5.The distance from chord PQ to center O is 12 mm.

14
1.ΔABC is isosceles (AB AC) 2.Circles P & Q, BC ║ PQ 3. ABC P, ACB Q 4. ABC ACB 5. P Q 6.AP AQ 7.PB CQ 8.Circle P Circle Q 1.Given 2.Given 3.║ Lines means corresponding s . 4.. 5.Transitive Property 6.. 7.Subtraction (1 from 6) 8.Circles with radii are .

Similar presentations

© 2023 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google