The radius of a circle is 2.5 cm. AB and CD are two parallel chords 2.7 cm apart. If AB = 4.8 cm then CD is equal
Answers
Answer
C=3cm
Step-by-step explanation:
Here, AB∥CD
AB=4.8cm and AM=MB=
2
AB
=2.4cm
OM and ON are perpendicular to AB and CD
In △AMO,
⇒ (OA)
2
=(AM)
2
+(OM)
2
[By Pythagoras theorem ]
⇒ (2.5)
2
=(2.4)
2
+(OM)
2
⇒ 6.25=5.76+(OM)
2
⇒ 0.49=(OM)
2
∴ OM=0.7cm
⇒ ON=MN−OM
⇒ ON=2.7−0.7
⇒ ON=2cm
In CNO,
⇒ (OC)
2
=(ON)
2
+(CN)
2
⇒ (2.5)
2
=(2)
2
+x
2
⇒ x
2
=6.25−4
⇒ x
2
=2.25
∴ x=1.5
⇒ CD=(1.5+1.5)cm
∴ CD=3cm
Answer:
CD = 4.8 cm
Step-by-step explanation:
Given, AB and CD are two parallel chords of a circle with centre O.
Now, in triangle AOB and triangle COD,
AO=CO (Radius of same circle)
BO=DO (Radius of same circle)
angle AOB = angle BOD (Vertically Opposite angles)
By SAS congruence rule,
triangle AOB is congruent to triangle BOD
=> AB = CD (by C.P.C.T)
therefore, CD = AB = 4.8 cm