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CBSE Class 10 Answered

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 ??
Asked by Kunwar Digvijay Singh Tanwar | 15 Mar, 2013, 02:18: PM
answered-by-expert Expert Answer
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. 
Answered by | 16 Mar, 2013, 05:57: AM

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