Page 1 :
B, MATHEMATICS, 898, Construction : A,0 and C, O are joined., D., rig, C., Proof : The reflex angle AOC at the centre and the angle ZABC on the circle, formed with circular arc ADC., . Reflex ZAỌC = 2ZABC, %3D, . ZABC - reflex ZAO ., (!), pe, Again, ZAOC is the angle at the centre andZADC is the angle on the circle former, with the circular arc ABC., .. ZAOC = 22ADC, 1., ZADC = – ZAOC, 2, (!1), 1., ZAOC, . From (i) and (ii), we get ZABC + ZADC = - reflex ZAOC +, %3D, 2, 2., 1., - (reflex ZAOC +ZAOC), %3D, 2., 1., x 4 right angles = 2 right angles., %3D, %3D, 2., Similarly by joining B,0 and D, 0; it can be proved that, ZBAD +ZBCD = 2 right, angles. (Proved), 10. Answer any one question :, 1 x 3 = 3, Two circles intersect each other at the points P and Q. If the diameters of the, two circles are PA and PB respectively, then prove that A, Q, B are coline, Q.1., (M.P. 2020), Solution : Given : Let two circles with centres O and O' intersect each other atPaie, Q. PA is a diameter of the circle with centre at O and PB is also a diameter of the Cher, with centre at O'., To Prove : A,Q,B are collinear.