Question

Chords AB and CD of lengths 24 cm and 10cm respectively are parallel andlie on the same side of the circle if the perpendicular distance between them is 7cm find the length of its diameter

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