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When a circle is drawn through each vertex of a right triangle the triangle's hypotenuse will be equal to?
Its diameter.
What if the altitude to the hypotenuse of a right triangle is the geometric mean between the segments on the hypotenuse?
Always true. To see this draw the circle which passes through the three points of the triangle. Reproduce the reflection of the triangle on the hypotenuse (which passes through the centre). Then use the theorem of intersecting chords of a circle to give the result immediately. It's also simply proved by algebra.
What is the hypotenuse of pi r squared?
The hypotenuse is the longest side of a right angle triangle The area of a circle is pi*radius2
How do you show that from the right angle vertex to the midpoint of the hypotenuse is half the length of the hypotenouse?
All right triangles inscribed in a circle have their vertices on the circle and the hypotenuse as the circle's diameter. Thus the midpoint of the hypotenuse is the center of the circle nd all points on the circle are eqully as far from the center even so the vertex of the right angle.
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.
When a circle is drawn through each vertex of a right triangle the triangle's hypotenuse will be equal to?
Its diameter.
What relationship does the hypotenuse have with the circle?
The hypotenuse has no intrinsic relationship to the circle. The hypotenuse is the side of a right triangle that is opposite to the right angle. You can draw a circle that has a hypotenuse as its diameter or its radius, but you can do that with any line segment. It would not be related in another way to the triangle.
What if the altitude to the hypotenuse of a right triangle is the geometric mean between the segments on the hypotenuse?
Always true. To see this draw the circle which passes through the three points of the triangle. Reproduce the reflection of the triangle on the hypotenuse (which passes through the centre). Then use the theorem of intersecting chords of a circle to give the result immediately. It's also simply proved by algebra.
What is the relationship between circles and triangles?
Circles and triangles are geometric shapes with distinct properties, but they can be related through various geometric principles. For example, a circle can be inscribed in a triangle or a triangle can be inscribed in a circle. Additionally, the circumcircle of a triangle is a circle that passes through all three vertices of the triangle. These relationships demonstrate the interconnected nature of geometric shapes and the principles that govern their properties.
Can there be a hypotenuse of a circle?
No. A hypotenuse is defined as the side opposite the right angle in a triangle that contains a right angle.
What is the hypotenuse of pi r squared?
The hypotenuse is the longest side of a right angle triangle The area of a circle is pi*radius2
How do you show that from the right angle vertex to the midpoint of the hypotenuse is half the length of the hypotenouse?
All right triangles inscribed in a circle have their vertices on the circle and the hypotenuse as the circle's diameter. Thus the midpoint of the hypotenuse is the center of the circle nd all points on the circle are eqully as far from the center even so the vertex of the right angle.
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.
The relationship between triangles and circles?
The three vertices of the triangle uniquely determine a circle that circumscribes the triangle. The three sides of the triangle uniquely determine the circle that inscribes the triangle.
What is the circumference of a triangle?
triangle does not have a circumference, a circle has a circumference. A triangle only has a hypotenuse (Pythagoras sort of stuff). The circumference of a circle is the perimeter of it, so, perhaps, if your teacher ask for the circumference of a triangle he/she might mean the perimeter of the triangle.
How do you find the length of the legs of a right triangle or the coordinate when you are given the coordinates of the hypotenuse on a graph?
You cannot. If you draw a circle with the given hypotenuse as the diameter then the right angle of the triangle can be at ANY point on the circumfeence of the circle. Therefore, the lengths of the two legs are indeterminate.
What cannot be made by a medium triangle and 2 small triangles?
A circle, for sure.
