The radius of à circle is 2.5 cm. AB, CF are two // chord 3.9 cm àpart. if AB=1.4 cm,find CF.
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Let center of circle be O
Draw a perpendicular line joining the chords passing through O
it meets AB at P
it meets CF at Q
PQ = 3.9
Let OP be x
OQ= 3.9-x
PA=1/2 AB = 0.7
OPA and OQC are right triangles
The radii are the hypotenuse
In triangle OPA OA^2=OP^2++PA^2
2.5^2=x^2+0.7^2
2.5^2-0.7^2=OP^2
6.25-0.49=OP^2
5.76=OP^2
OP=2.4
CQ=3.9-2.4= 1.5
similarly
2.5^2= CQ^2+(1.5)^2
CQ^2=2.5^2-1.5^2
cq^2=4
CQ=2
2*Cq=CF
CF=4 cm
Draw a perpendicular line joining the chords passing through O
it meets AB at P
it meets CF at Q
PQ = 3.9
Let OP be x
OQ= 3.9-x
PA=1/2 AB = 0.7
OPA and OQC are right triangles
The radii are the hypotenuse
In triangle OPA OA^2=OP^2++PA^2
2.5^2=x^2+0.7^2
2.5^2-0.7^2=OP^2
6.25-0.49=OP^2
5.76=OP^2
OP=2.4
CQ=3.9-2.4= 1.5
similarly
2.5^2= CQ^2+(1.5)^2
CQ^2=2.5^2-1.5^2
cq^2=4
CQ=2
2*Cq=CF
CF=4 cm
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