Question

ar one end A of a diameter AB of a circle of radius 13 cm, tangent XAY is drawn to the circle. A
chord CD is parallel to XY and is at a distance of 18 cm from A. What will be the length of CD?
AOB is a diameter of a circle with
Ire​

Answer 1

Answer:

CD=2×MC

given that:-

radius of circle = 5cm=AO=OC

AM=8CM

and

AM=OM+AO

THEN

OM =AM-AO

Put the vlues in this equation given above

We Get

=> OM= (8-5) =3CM

we know that;-

OM is perpendicular to the chord CD.

In∆OCM <OMC=90°

using Pythagoras theorem

we get,

OC²=OM²+MC²

.

\begin{gathered} {(mc)}^{2} = {(omc)}^{2} - {(om)}^{2} \\ = > {(mc)}^{2} = {5}^{2} - {3}^{2} \\ = > {(mc)}^{2} = 25 - 9 \\ = > {(mc)} = \sqrt{16 } \\ = > {(mc)} = 4cm\end{gathered}(mc)2=(omc)2−(om)2=>(mc)2=52−32=>(mc)2=25−9=>(mc)=16=>(mc)=4cm

Hence,

CD= 2 ×CM  = 8 cm

I HOPE ITS HELP YOU DEAR,

THANKS