Question

two chord Ab and CD are at a distance of 4cm from the centre . is AB = CD state true or false and justify your answer

Answer 1

yes true because..=>join OA,OB,OC AND OD..and draw a perpendicular OP on AB and OQ on CD..so length of OP and OQ is given i.e.4cm...so they are equal..now..we also know that perpendicular drawn from a centre to the chord bisects the chord..so AP=PB and CQ=QD..now in Triangle OPB and OQD..angle OPB=angle OQD=90degree..OB=OD(radius) and PO=OQ(proved above)..so both the triangles are equal by RHS..so PB=QD..by C.P.C.Tnow 2PB=2QD=AB=CD...so hence proved!!