Question

Help me out!!!!

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Answer 1

ANSWER :

GIVEN :

in circle at centre o

MN and RS are chords such that

angle OPM=angle OPR

TO PROVE :

MN=RS

CONSTRUCTION :

draw OA perpendicular to MN and OB perpendicular to RS

PROOF :

In ∆AOP and ∆BOP

angle OAP = angle OBP.......(Each 90°(by construction))

also

angle OPA= angle OPB.........(Given)

also

OP=OP ......(common side)

hence by AAS congruence criteria

∆OAP is congruent to ∆OBP

so by CPCT

OA=OB

Now in circles

by the theorem that if two chords are equidistant from centre of a circle then they are equal..

as OA = OB

=> MN=RS

HENCE PROVED

NOTE:

while solving such questions

learn to apply the needed theorems