Find the area of the square that can be inscribed in a circle of radius 6 cm6 cm6 cm.
Answer:
72 cm272 cm272 cm2
- Let us draw a circle with OOO as a center and radius 6 cm6 cm6 cm.
Now, let us draw a square ABCDABCDABCD inside the circle. We see that the diagonal of the square is equal to the diameter of the circle.
Radius of the circle = 6 cm6 cm6 cm
So, diameter of the circle =2×=2×=2× Radius =2×6 cm=12 cm=2×6 cm=12 cm=2×6 cm=12 cm
Therefore, diagonal of the square =12 cm=12 cm=12 cm - Using Pythagores' theorem in △ABC△ABC△ABC, we have [Math Processing Error]
- We know, [Math Processing Error]
- Thus, the area of the square that can be inscribed in a circle of radius 6 cm6 cm is 72 cm272 cm2.