Find the Area of a Right Triangle Inscribed in a Circle with Diameter 12 cm.

First, we need to recognize that this is a right-angled triangle inscribed in a circle. BC is the diameter of the circle, which means angle BAC is a right angle (90°).

We’re given that BC = 12 cm, which is the diameter of the circle. This means the radius of the circle is 6 cm.

In a right-angled triangle, we can use the formula:
Area = * base * height

We know the base (BC) is 12 cm. We need to find the height, which is the radius of the circle perpendicular to BC.

The radius perpendicular to BC is 6 cm (as we found in step 2).

Now we can apply the formula:
Area = * 12 * 6

Let’s calculate:
Area = * 72 = 36