# A right triangle ABC is inscribed in a circle with centre O, as shown in the following diagram. A and C are endpoints of a diameter, and B is a point that lies on the circumference. AC measures #sqrt(277)# cm, and side BC measures 5 cm less than AB?->

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What is the area of the shaded region in the diagram?

What is the area of the shaded region in the diagram?

##### 1 Answer

#### Explanation:

As the shaded region, the triangle, and the semicircle not containing the triangle partition the circle, we know that the area of the shaded region is the difference between the area of the circle and the sum of the areas of the right triangle and the remaining semicircle. Thus, if we can calculate those areas, we are done.

First, note that as the triangle is a right triangle, we have

Substituting in

#=(5+-23)/2#

As

Again, as the triangle is a right triangle, we can treat

Next, as

Using our initial observation, we can now directly calculate the area