Question

answer this step by step​

Answer 1

1

Secondary SchoolMath 5 points

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