two chords AB , CD of length 24cm , 10cm , respectively of a circle are parallel if the chords lie on the same side of centre and the distance between them is 7cm . then length of a diameter of the circle
Answers
Answer:
diameter=26
Step-by-step explanation:
Given two chords AB and CD of lengths 24 cm and 10 cm respectively of a circle are parallel . 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.
Let OF=x gives OE=7+x
Hence, ΔOED and ΔOFB both are right angled triangle.
By Pythagoras theorem
In ΔOED, OD^{2}=OE^{2}+ED^{2}OD
2 =OE
2 +ED
2⇒ r^{2}=(7+x)^{2}+5^{2}r
2 =(7+x)
2 +5 2
In ΔOFB, OB^{2}=OF^{2}+FB^{2}OB
2 =OF
2 +FB
2⇒ r^{2}=x^{2}+12^{2}r
2 =x
2 +12
2
From above two equations,
(7+x)^{2}+5^{2}=x^{2}+12^{2}(7+x)
2+5 2 =x
2 +12
2
⇒ (49+x^2+14x)+25=x^{2}+144(49+x)(2 +14x)+25=x
2 +144
⇒ 14x=7014x=70 ⇒ x=5
∴ r^{2}=5^{2}+12^{2}=25+144=169r
2
=5
2
+12
2
=25+144=169
⇒ r=13
Hence, diameter is 2r=2(13)=26 cm