Public
The diameter of the circle circumscribed around a right triangle is the hypotenuse of the triangle. We apply the Pythagorean theorem to find the hypotenuse.
Join our group
Public
Let \( a = 8 \) cm and \( b = 15 \) cm be the legs of the right triangle. The hypotenuse \( c \) is given by:
Join our group
Public
\[
Join our group
Public
c = \sqrt{a^2 + b^2} = \sqrt{8^2 + 15^2} = \sqrt{64 + 225} = \sqrt{289} = 17 \ \text{cm}
Join our group
Public
\]
Join our group
Public
Thus the diameter of the circumscribed circle is 17 cm.
Join our group
Public
\[
Join our group
Public
\boxed{17 \ \text{cm}}
Join our group
Public
\]
Join our group
Public
Question:** A square with a side length of 10 cm is inscribed in a circle. Determine the area of the circle.
Join our group
Public
Solution:
Join our group
Public
When a square is inscribed in a circle the diameter of the circle is equal to the diagonal of the square. We first calculate the diagonal of the square.
Join our group
