Albert said:24 points $A_1,A_2,-----,A_{24}$ equally divide the circumference of circle $O$
,any three of the 24 points will determine an inscribed triangle,
now how many triangles can be proclaimed as right angled ?
HallsofIvy said:I think you mean "diameter" rather than "diagonal". Albert, the measure of an angle inscribed in a circle is 1/2 the measure of the arc it subtends. In order that the angle be right, that arc subscribed must be a semicircle so that the hypotenuse of the triangle is a diameter of the circle.
HallsofIvy said:I think you mean "diameter" rather than "diagonal". Albert, the measure of an angle inscribed in a circle is 1/2 the measure of the arc it subtends. In order that the angle be right, that arc subscribed must be a semicircle so that the hypotenuse of the triangle is a diameter of the circle.
A right angled triangle is a triangle with one angle measuring 90 degrees. This can be determined by using the Pythagorean theorem, which states that in a right angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
No, not all triangles can be right angled. Only a triangle with one angle measuring 90 degrees can be considered right angled. Triangles with three acute angles (all angles less than 90 degrees) or with one obtuse angle (greater than 90 degrees) cannot be right angled.
The number of right angled triangles that can be formed from a set of given points is dependent on the arrangement of the points. In general, there can be multiple right angled triangles formed from a set of points, but it is not possible to determine an exact number without knowing the specific coordinates of the points.
No, a triangle can only have one right angle. This is because the sum of the angles in a triangle is always 180 degrees, so if one angle is 90 degrees, the other two angles must add up to 90 degrees as well.
No, a right angled triangle is not necessarily the same as an isosceles triangle. An isosceles triangle has two sides that are equal in length, while a right angled triangle has one angle measuring 90 degrees. However, it is possible for a right angled triangle to also be isosceles if the two shorter sides are equal in length.