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Central Angle : an angle with its vertex at the center of the circle

Inscribed and Central Angle. Central Angle : an angle with its vertex at the center of the circle. Inscribed Angle : an angle whose vertex on a circle and whose side contain chord of the circle. Created by ﺠﻴﻄ for Mathlabsky.wordpress.com.

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Central Angle : an angle with its vertex at the center of the circle

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  1. Inscribed and Central Angle Central Angle : an angle with its vertex at the center of the circle Inscribed Angle : an angle whose vertex on a circle and whose side contain chord of the circle Created by ﺠﻴﻄ for Mathlabsky.wordpress.com Created by ﺠﻴﻄ for Mathlabsky.wordpress.com

  2. Inscribed and Central Angle A B AOB = Central Angle ACB = Inscribed Angle O • b a C c Theorem a +  b =  c x Proof :

  3. AOB = 2 ACB A Let ACO = p, and BCO = q p O 2p p C D OC = OA (radius) ACO =  CAO q 2q q OC = OB (radius) BCO =  CBO B • b AOD = 2p & BOD = 2q a c AOB = 2p + 2q & ACB = p + q  AOB = 2 ACB

  4. ACB = ADB A B O • AOB = 2 ACB AOB = 2 ADB ACB = ADB C D “If two inscribed angles intercept the same arc, than the angle are congruent”

  5. ABC = 900 A AOC = 1800 B O AOC = 2 ABC • C ABC = 900 “An angle inscribed in a semicercle is a right angle”

  6. BAD + BCD = 180 A D 2 Let m1=2x 3 O  m2 = x and m3 = (360 – 2x) 1 4 C • m3 = (360 – 2x) B  m4 = ½(360 – 2x)  m4 = 180 – x m2 + m4 = x + (180 – x) BAD + BCD = 180 “If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary”

  7. A D 3 3 E 1 1 AEB = CED 2 2 ABD = ACD B • C BAC = BDC E E  ABE  CDE  1 1 3 2 2 3 B C A D

  8. AEB = ½ AOB+ ½ COD A Let AOB = x and COD = y D E  ACB = ½ x ● O y X C  DBC = ½ y • B A E ½ x C  AEB = ½ x + ½ y ½ y B AEB = ½ AOB+ ½ COD

  9. AEB = ½ AOB - ½ COD A Let AOB = x and COD = y D E O y x  ADB = ½ x C  DBC = ½ y • B A D ½ x E  AEB = ½ x - ½ y ½ y B AEB = ½ AOB - ½ COD

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