In a circular lawn, there is a 16 m long path in the form of a chord. If the path is 6 m away from the center of the lawn, then find the radius of the circular lawn.

From given figure , we can see that
Let AB = 16 m , OM = 6 m , AM = BM = 8 m and OA = r
In triangle AMO ,
By pythagoras theorem ,
OA² = AM² + OM²
OA² = 8² + 6² = 64 + 36
OA² = 100 ⇒ OA = √ 100 = 10
∴ OA = r = 10 m
The radius of the circular lawn = 10 m