Question

28. A1, A2, A3, ... ... A11, A12 are 12 distinct points equally spaced in the same order on the circumference of a circle. Find the distinct number of triangles which can be formed using these points as vertices such that their circumcenter lies on one of the sides of the triangle? ​

Answer 1

Given : A1, A2, A3, ... ... A11, A12 are 12 distinct points equally spaced in the same order on the circumference of a circle.  

To Find : the distinct number of triangles which can be formed using these points as vertices such that their circumcenter lies on one of the sides of the triangle

Solution:

There are 12 points  equally spaced  

Hence there will be 6 diameters

as  circumcenter lies on one of the sides of the triangle hence triangle must be a right angle triangle hence one side will be diameter

Now  after having one diameter there will be 10 point left

Hence 10 triangle with one diameter hence

6 * 10  = 60 triangles will be formed

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