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Yes. It follows from one of the circle theorems which states that the angle subtended in a semicircle is a right angle.

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Q: When a triangle with one side length the diameter of a circle is inscribed in that circle does it have to be a right triangle?
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How do you work out the area of a circle in a square?

The formula for the area of a circle is pi x radius2. The radius is half the diameter, and the diameter of an inscribed circle is the same as the length of a side of the square.The formula for the area of a circle is pi x radius2. The radius is half the diameter, and the diameter of an inscribed circle is the same as the length of a side of the square.The formula for the area of a circle is pi x radius2. The radius is half the diameter, and the diameter of an inscribed circle is the same as the length of a side of the square.The formula for the area of a circle is pi x radius2. The radius is half the diameter, and the diameter of an inscribed circle is the same as the length of a side of the square.


What is the formula for equillateral triangle?

There are different formula for: Height, Area, Perimeter, Angle, Length of Median Radius of inscribed circle Perimeter of inscribed circle Area of inscribed circle etc.


When a circle is drawn through each vertex of a right triangle the triangles hypotenuse will be equal to what?

The length of the circle's diameter


What shows an equilateral triangle inscribed in a circle?

An equilateral triangle inscribed in a circle has three sides that are equal in length and three angles that are each 60 degrees. The center of the circle is also the intersection point of the triangle's perpendicular bisectors.


How would you construct a right triangle given the length of a leg and the radius of the circumscribed circle?

To construct a right triangle given the radius of the circumscribed circle and the length of a leg, begin with two ideas. First, the diameter of the circle is equal to twice the radius. That's pretty easy. Second, the diameter of the circle is the length of the hypotenuse. The latter is a key to construction. Draw your circle, and draw in a diameter, which is the hypotenuse of the right triangle, as was stated. Now set you compass for the length of the leg of the triangle. With this set, place the point of the compass on one end of the diameter (the hypotenuse of your triangle), and draw an arc through the circumference of the circle. The point on the curve of the circle where the arc intersects it will be a vertex of your right triangle. All that remains is to add the two legs or sides of the triangle. Draw in line segments from each end of the hypotenuse (that diameter) to the point where your arc intersected the curve of the circle. You've constructed your right triangle. Note that any pair of lines that is drawn from the ends of the diameter of a circle to a point on the curve of the circle will create a right triangle.

Related questions

If you have a circle inscribed in a square what is the diameter congruent to?

The diameter of the circle equals the length of a side of the square


How do you work out the area of a circle in a square?

The formula for the area of a circle is pi x radius2. The radius is half the diameter, and the diameter of an inscribed circle is the same as the length of a side of the square.The formula for the area of a circle is pi x radius2. The radius is half the diameter, and the diameter of an inscribed circle is the same as the length of a side of the square.The formula for the area of a circle is pi x radius2. The radius is half the diameter, and the diameter of an inscribed circle is the same as the length of a side of the square.The formula for the area of a circle is pi x radius2. The radius is half the diameter, and the diameter of an inscribed circle is the same as the length of a side of the square.


What is the formula for equillateral triangle?

There are different formula for: Height, Area, Perimeter, Angle, Length of Median Radius of inscribed circle Perimeter of inscribed circle Area of inscribed circle etc.


If a square is inscribed in a circle the diameter of the circle is congruent to?

The diameter of the circle is congruent to the length of the diagonal of the inside square. If you know the length of one side of the square, you can use pythagorean's theorem to solve for its diagonal (hypotenuse) and thusly the square's diameter.


When a circle is drawn through each vertex of a right triangle the triangles hypotenuse will be equal to what?

The length of the circle's diameter


Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius a?

The largest rectangle would be a square. If the circle has radius a, the diameter is 2a. This diameter would also be the diameter of a square of side length b. Using the Pythagorean theorem, b2 + b2 = (2a)2. 2b2 = 4a2 b2 = 2a2 b = √(2a2) or a√2 = the length of the sides of the square The area of a square of side length b is therefore (√(2a2))2 = 2a2 which is the largest area for a rectangle inscribed in a circle of radius a.


What shows an equilateral triangle inscribed in a circle?

An equilateral triangle inscribed in a circle has three sides that are equal in length and three angles that are each 60 degrees. The center of the circle is also the intersection point of the triangle's perpendicular bisectors.


How would you construct a right triangle given the length of a leg and the radius of the circumscribed circle?

To construct a right triangle given the radius of the circumscribed circle and the length of a leg, begin with two ideas. First, the diameter of the circle is equal to twice the radius. That's pretty easy. Second, the diameter of the circle is the length of the hypotenuse. The latter is a key to construction. Draw your circle, and draw in a diameter, which is the hypotenuse of the right triangle, as was stated. Now set you compass for the length of the leg of the triangle. With this set, place the point of the compass on one end of the diameter (the hypotenuse of your triangle), and draw an arc through the circumference of the circle. The point on the curve of the circle where the arc intersects it will be a vertex of your right triangle. All that remains is to add the two legs or sides of the triangle. Draw in line segments from each end of the hypotenuse (that diameter) to the point where your arc intersected the curve of the circle. You've constructed your right triangle. Note that any pair of lines that is drawn from the ends of the diameter of a circle to a point on the curve of the circle will create a right triangle.


What is the radius of a circle that has a right angle triangle located on its entire diameter with legs of 6 and 8 cm?

The diameter of the circle will also be the triangle's hypotenuse so use Pythagoras theorem to find the hypotenuse's length and half the length which will result as a radius of 5 cm.


How do you find the diameter of a circle with the width and length?

The width, or the length of a circle are its diameter.


What is the length of the diameter of 9 in?

the diameter is the length. the diameter means the length of across the circle. it means the longest length across the circle. the radius is halfthe diameter


Which is true about a circle is inscribed in a hexagon?

The radius of a circle inscribed in a regular hexagon equals the length of one side of the hexagon.