A 16 cm by 12 cm rectangle is inscribed in a circle.. find the radius of the circle.
~answer
Well, I would tell you the answer, but I seem to have misplaced my measuring tape. I guess I'll just have to clown around and make something up! How about we call the radius of the circle "R", and the rectangle is inscribed in the circle so that the longer side of the rectangle is a diameter. In that case, the diameter of the circle would be equal to the length of the longer side of the rectangle, which is 16 cm. So, if we divide the diameter by 2, we get the radius. Ta-da! The radius would be 8 cm. However, remember that this is just clown logic, so it's always better to consult a real mathematician for accurate calculations.
To find the radius of the circle, we can use the Pythagorean theorem.
Let's label the sides of the rectangle as follows:
- The length of the rectangle (16 cm) will be the base.
- The width of the rectangle (12 cm) will be the height.
- The hypotenuse of the right-angled triangle formed inside the rectangle will be the diameter of the circle.
According to the Pythagorean theorem, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides of the right-angled triangle.
Let's calculate the length of the hypotenuse using Pythagorean theorem:
h^2 = 16^2 + 12^2
h^2 = 256 + 144
h^2 = 400
Taking the square root of both sides:
h = √400
h = 20 cm
The hypotenuse is equal to the diameter of the circle, so the radius is half the diameter.
Therefore, the radius of the circle is 20 cm / 2 = 10 cm.
To find the radius of the circle, we need to use the relationship between the diagonal of the rectangle and the diameter of the circle.
The diagonal of the rectangle is the diameter of the circle, so we can find the diagonal by using the Pythagorean theorem.
The length of the diagonal can be found using the formula:
diagonal = square root of (length^2 + width^2)
In this case, the length is 16 cm and the width is 12 cm.
So, we can calculate the diagonal:
diagonal = square root of (16^2 + 12^2)
diagonal = square root of (256 + 144)
diagonal = square root of 400
diagonal = 20 cm
Since the diagonal is equal to the diameter of the circle, the radius will be half of the diameter. Therefore, the radius of the circle is:
radius = 20 cm / 2
radius = 10 cm
So, the radius of the circle is 10 cm.
i think my question in rectangle.. about it..
make a sketch
draw in the diagonal, it will pass through the centre at its midpoint.
Use Pythagoras, you will see a right-angled triangle.