How Do You Prove A Chord Bisects An Angle In A Circle?
Draw the diagram and mark O as the centre of the circle OA = OB (radii) Hence triangle AOB is isosceles angle OAB = angle OBA = x, say BE is the tangent at B and so OB is perpendicular to BE (radius is perpendicular to tangent at point of contact) angle OBE = 90° angle ABE = 90° – x Triangle ABE is right-angled at E (given) angle EAB = 180° – (90° + 90° – x) = x Thus angle EAB = angle OAB (= x) Hence AB bisects angle CAE
