Theorem 10.4

Transcript

Theorem 10.4 The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord. Given : A circle with center at O. AB is chord of circle & OX bisects AB i.e. AX = BX To Prove : OX AB Proof : In AOX = BOX OA = OB OX = OX AX = BX AOX BOX AXO = BXO In line AB, Hence, AXO and BXO form linear Pair AXO + BXO = 180 AXO + AXO = 180 2 AXO = 180 AXO = 180 2 AXO = 90 AXO = BXO = 90 OX AB Hence, Proved.