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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.
What is angle inscribed in semi circle called?
An angle inscribed in a semicircle is called a right angle. According to the inscribed angle theorem, any angle formed by two points on the circumference of a semicircle, with the vertex at the circle's center, measures 90 degrees. This property holds true for any triangle inscribed in a semicircle, confirming that the hypotenuse is the diameter of the circle.
Is length of tangent to a circle from an external point is always greater than radius of circle?
Yes, the length of the tangent from an external point to a circle is always greater than the radius of the circle. This is because the tangent line is perpendicular to the radius at the point of contact, forming a right triangle where the radius is one leg and the tangent is the hypotenuse. Since the hypotenuse is always longer than either leg in a right triangle, the tangent length must exceed the radius.
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 is Hippocrates theorem about the circle?
Hippocrates' theorem states that if a right triangle is inscribed in a circle, the area of the circle can be expressed as the sum of the areas of the squares constructed on the two legs of the triangle. This theorem illustrates a geometric relationship between the triangle and the circle, highlighting that the area of the circle (when a right triangle is inscribed) equals the combined areas of the squares on its two shorter sides. It serves as an early insight into the connection between geometry and area.
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.
What is angle inscribed in semi circle called?
An angle inscribed in a semicircle is called a right angle. According to the inscribed angle theorem, any angle formed by two points on the circumference of a semicircle, with the vertex at the circle's center, measures 90 degrees. This property holds true for any triangle inscribed in a semicircle, confirming that the hypotenuse is the diameter of the circle.
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.
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.
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.
