Chapter 21. Circles – Summary Focus on UNDERSTANDING, not MEMORIZING Notes β Sector Area & Arc Length Arc Length = Part of the circumference π΄ππ πΏππππ‘β = 2πr X π¨ππππ πππ Sector area = Part of the area ππππ‘ππ π΄πππ = πr ) X π¨ππππ πππ *+,-. Insight: The /01 represents the fraction/portion of the circle you’re finding. You can use this to find what fraction/portion of the circle is represented by the sector/arc. Example ____. ___________________________ πΆ 140° π΄ © π΅ The circle above has a center at point B. What fraction of the circle is the area of the sector formed by the minor angle ABC? # = 2ππ ∗ πππ π΄πΆ πππ è πππ πππ π = ππ = Fraction of the circle represented by the arc β‘ Inscribed Angle Definition: Two angles (central & inscribed) sharing the same ending points have the relationships below • Inscribed angle = ½ Central angle Example ____. ___________________________ !"° _____° What is the measure of the missing angle? Ans: 45 © AdmissionHackers.com - All rights reserved. Do not share, copy, reproduce or sell any part of this document unless you have written permission from AdmissionHackers.com. All infringements will be prosecuted. If you are the personal owner of the AdmissionHackers.com End User License then you may use it for your own use but not for any other purpose. Chapter 21. Circles – Summary Focus on UNDERSTANDING, not MEMORIZING Notes β’ Equations Of A Circle On The Coordinate Plane Equation: (π₯ − β)) + (π¦ − π)) = π ) *If not in this form, you must complete the square to identify the center and the radius. Example ____. ___________________________ π₯ ) + 6π₯ + π¦ ) − 16π¦ = 71 What is the radius and center of the circle shown above? Ans: C = (-3,8) R = 12 β£ Circle Characteristics 1) Inscribed triangle with a diameter is always a right triangle. Example ____. ___________________________ 2) Radius + Tangent line = Perpendicular Example ____. ___________________________ B B 3 5 C 8 A C In the figure above, C represents the center of the circle. What is the area of the inscribed triangle? In the figure above, C represents the center of the circle. If the radius has the same measures as the segment ???? π΄π΅ that is tangent to the circle, ???? ? what is the length of π΄πΆ Ans: 6 © AdmissionHackers.com - All rights reserved. Do not share, copy, reproduce or sell any part of this document unless you have written permission from AdmissionHackers.com. All infringements will be prosecuted. If you are the personal owner of the AdmissionHackers.com End User License then you may use it for your own use but not for any other purpose. Ans: 8√2 Chapter 21. Circles – Summary Focus on UNDERSTANDING, not MEMORIZING Notes β€ Distance Formula Rule: Use the distance formula to find the distance between two points π = A(π₯) − π₯2 )) + (π¦) − π¦2 )) Example ____. ___________________________ What is the distance between the coordinates (2,3) and (-2,7)? Ans: 4√2 © AdmissionHackers.com - All rights reserved. Do not share, copy, reproduce or sell any part of this document unless you have written permission from AdmissionHackers.com. All infringements will be prosecuted. If you are the personal owner of the AdmissionHackers.com End User License then you may use it for your own use but not for any other purpose.
