AB and CD are two parallel chords on the same side of the centre of a circle of
length 24cm and 10cm respectively, if the diameter of the circle is 26cm find the
distance between the chords
Answers
Answer: 26cm
Step-by-step explanation:Find the diameter of the circle
According to the question, the figure looks like
Let
OF=x
gives
OE=7+x
Hence,
△OED and ΔOFB
both are right-angled triangles.
By Pythagoras theorem
In
ΔOED,OD
2
=OE
2
+ED
2
⇒r
2
=(7+x)
2
+5
2
In
ΔOFB,OB
2
=OF
2
+FB
2
⇒r
2
=x
2
+12
2
2r=2(13)=26cm
Step 2 of 2
From above two equations,
(7+x)
2
+5
2
=x
2
+12
2
⇒(49+x
2
+14x)+25=x
2
+144
⇒14x=70⇒x=5
∴r
2
=5
2
+12
2
=25+144=169
⇒r=13
Hence, diameter is
2r=2(13)=26cm
Answer: 7 cm
Step-by-step explanation: if the chord lie on the same side of the center and the distance between them is 7 cm. we have to find the length of diameter. As we know the line passing through center on the chord perpendicular bisect the chord. Hence, ΔOED and ΔOFB both are right angled triangle