Fig. 10.25A circular park of radius 20m is situated in a colony. Three

1.	Fig. 10.25A circular park of radius 20m is situated in a colony. Three boys Ankur, Syed andDavid are sitting at equal distance on its boundary each having a toy telephone inhis hands to talk each other. Find the length of the string of each phone.
Answer» let AB,BC,AC be the length of each string AB=BC=AC [ equal arcs subtends equal chords] construction : draw perpendicular bisector of AB,BC,AC •AO=OB=OC(equal radii)=20m Centroid - the centroid of a circle is the point located at 2/3 of the distance from the vertex along a median AO/OD=2/1 [centroid of a circle divides a median in the ratio of 2:1 20/OD=2/120/2 = OD10m=OD in∆BOD(BD)^2=(20)^2-(10)^2BD=√400-100BD=√300BD=10√3 a line from a centre to the chord is the perpendicular bisetcor of the chord BD=DC BC=2×10√3=20√3m AB=BC=CA=20√3m hence length of each string are 20√3m hit like if you find it useful any other methods the other method

Fig. 10.25A circular park of radius 20m is situated in a colony. Three boys Ankur, Syed andDavid are sitting at equal distance on its boundary each having a toy telephone inhis hands to talk each other. Find the length of the string of each phone.

Answer»

let AB,BC,AC be the length of each string

AB=BC=AC [ equal arcs subtends equal chords]

construction : draw perpendicular bisector of AB,BC,AC

•AO=OB=OC(equal radii)=20m

Centroid - the centroid of a circle is the point located at 2/3 of the distance from the vertex along a median

AO/OD=2/1 [centroid of a circle divides a median in the ratio of 2:1

20/OD=2/120/2 = OD10m=OD

in∆BOD(BD)^2=(20)^2-(10)^2BD=√400-100BD=√300BD=10√3

a line from a centre to the chord is the perpendicular bisetcor of the chord

BD=DC

BC=2×10√3=20√3m

AB=BC=CA=20√3m

hence length of each string are 20√3m

hit like if you find it useful

any other methods

the other method