Question

O is the centre of a circle . OM & ON are the perpendicular distances from O upon two chords AB & CD .If OM=0N,then prove that AB=CD. (please explain with the help of diagram.)​

Answer 1

hey mate! !

here is your answer...

»in the diagram as you can see

given,circle (O,r)

•AB and CD are 2 chords of circle

•OM and ON are perpendicular from center to the chords

According to marks there are 2 solutions :

1.)if question is of 2 marks ;just make diagram and write the theorem (equal chords of the circle are equidistance from the center of circle)

2.)if question is of 3 to 5 marks then to prove it.

›in given diagram

first AM=BM and CN=DN(perpendicular from the center bisect the chord)

In ∆AMO and ∆CNO

OM=ON(given)

AO=CO(radii of circle)

angle CNO=angle AMO(each of 90°)

∆AMO~∆CNO(RHS)

therefore,

AM=CN________(C.P.C.T)

so we can prove that AB=CD (if halves of two lines are equal so those lines are equal)

hence, proved.....

★★Hope it will be helpful for you★★

Answer 2

Answer: c

Step-by-step explanation:

Edgenuity