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It a right triangle is inscribed in a circle the the what is a diameter of the circle?
The diameter is the distance across the centre of the circle.
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?
Yes. It follows from one of the circle theorems which states that the angle subtended in a semicircle is a right angle.
What theorem did Thales gave to geometry?
The theorem where a triangle inscribed in a circle is right if and only if one of the legs is a diameter.
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.
How do you work out the radius of a circle from a chord?
This is hard to explain without a diagram, but draw a circle with a chord through it. Now draw a line from the center of the circle to the center of the chord and you'll have a right angle. Draw the hypotenuse of this new right triangle, which just happens to be the radius. I took geometry last year, so I'm kind of stuck at this point, but I know you have to work with that right triangle.
An isosceles right triangle is inscribed in a circle Find the radius of the circle if one leg of the triangle is 8 cm?
First you half all the sides, so 4cm, them you multiply by pi, giving the radius as 12pi, or 12.56637061
It a right triangle is inscribed in a circle the the what is a diameter of the circle?
The diameter is the distance across the centre of the circle.
When a right triangle is inscribed in a circle will one of the legs of the triangle always be the diameter of a circle?
yes. the leg of the triangle has to be formed different because of the circle
What is angle of inscribed in semi circle?
A right angle triangle can fit into a semi-circle
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?
Yes. It follows from one of the circle theorems which states that the angle subtended in a semicircle is a right angle.
What theorem did Thales gave to geometry?
The theorem where a triangle inscribed in a circle is right if and only if one of the legs is a diameter.
What is the slant height formula?
The slant height of a cone is given by the formula , where r is the radius of the circle and h is the height from the center of the circle to the apex of the cone.It is trivial to see why this formula holds true. If a right triangle is inscribed inside the cone, with one leg of the triangle being the line segment from the center of the circle to its radius, and the second leg of the triangle being from the apex of the cone to the center of the circle, then one leg will have length h, another leg will have length r, and by the Pythagorean Thereon, r2 + h2 = d2, and gives the length of the circle to the apex of the cone.
Is a parallelogram inscribed in a circle always a rectangle?
Yes. The corners must be right angles for it to be inscribed on the circle.
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.
An equilateral triangle surrounds a circle of radius 10 cm and is itself surrounded by a larger circle Find the radius of the bigger circle?
Make a sketch of the situation. From a corner of the equilateral triangle draw a radius of the large circle, and from an adjacent side draw a radius of the smaller circle. You should have formed a small right-angled triangle with a known side of 10cm. and known angles of 30o, 60o and 90o. (The interior angles of an equilateral triangle are each 60o.) The hypotenuse is the unknown radius of the larger circle. But since cos 60 = 0.5, it is evident that the hypotenuse is 20cm. long.
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.
A right triangle is insribed in a circle of radius 3 the length of the hypotenus of the right triangle is?
Pythagoras! Two sides of the triangle must each be equal to the radius, ie 3 so Hypotenuse = sqrt(3^2 + 3^2) =sqrt 18 = 4.243
