In the figure above, the radius of the circle with center O is 1 and BC = 1. What is the area of triangular region ABC ?

Solution:

When a triangle is inscribed in a circle with one of the sides as the diameter of the circle, then the side of the triangle which is the diameter of the circle subtends a 90° at the circumference. The diagram above reveals that.

In other words triangle ABC is a right angled triangle with angle ∠ABC = 90°. Since it is a right angled triangle we can write:

AC² = BC²  + AB²

AC = 2 and BC =1 

Therefore 

AB = √AC² - BC² = √2² - 1²

AB = √4 -1 =√3

Area of the Triangle = (1/2)(Base)(Height)

=(1/2)(AB)(BC)

=(1/2)(√3)(1)

Area of the Triangle = √3/2 units

In the figure above, the radius of the circle with center O is 1, and BC = 1. What is the area of triangular region ABC?

Summary:

If the radius of the circle with center O is 1 and BC = 1 then the area of triangular region ABC is √3/2.