Q.2. A circular park of radius 25 cm is situated in a colony. three giirls ankita , anvita & goomal are siting on its boundary at equal distances. All the three girls having toy phone to talk with each other connected with string . Find the distance of the string between ankita & anvita ??

The girls are sitting on the circumference of the circle and they are equidistant from one another. 

radius of the circle = 25cm. 

Since they are sitting equidistant from one another, the angle subtended by them at the center would also be same i.e. 360/3 = 180 degree. 

 

Now, consider the circle O with A, B and C representing the 3 girls. Now, angle AOB = BOC = COA = 120 degree. 

 

Join AB. Draw a perpendicular OM from O to AB which intersects AB . 

Since, a perpendicular from the center of the circle to a chord bisects it as well as bisects the angle at the center. So, AM = MB and angle AOM = angle MOB = 120/2 = 60. 

 

Now in triangle AOM

sin60 = AM/AO

sqrt(3)/2 = AM/25

AM = 21.65 cm

 

Hence, AB = 2*AM = 2*21.65 = 43.30cm

So, the length of the string would be 43.30cm.