Question

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 .find the diameter of the circle.

Answer 1

Answer:

Diameter is 26 cm

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, $OD^{2}=OE^{2}+ED^{2}$

            ⇒ $r^{2}=(7+x)^{2}+5^{2}$

In ΔOFB, $OB^{2}=OF^{2}+FB^{2}$

            ⇒ $r^{2}=x^{2}+12^{2}$

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)=26 cm