out of two congruent chords of a circle distance
of one chord from the centre is 4cm then find
the distance of the other chord from the centre
with reson.
Answers
Step-by-step explanation:
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Answer:
Given- AB&CD are chords of a circle and they are equidistant (4cm) from the centre O.
To find out- Whether AB=CD.
Solution-
OM and ON are perpendiculars=4cm from O to AB & CD, respectively.
∴ They bisect AB & CD
i.e AM=
2
1
AB & DN=
2
1
DC
∠OMA=∠OND=90
o
.
Now, between the ΔAOM & △DON we have, OM=ON=4cm ...(given),
∠OMA=∠OND=90
o
OA=OD ...(radii of the same circle).
∴ΔAOM≡ΔDON ...(RHS test).
∴AM=DN⟹AB=DC.
So, the statement is true.