Search results
Results from the WOW.Com Content Network
The nine-point circle is tangent to the incircle and excircles. In geometry, the nine-point circle is a circle that can be constructed for any given triangle. It is so named because it passes through nine significant concyclic points defined from the triangle. These nine points are: [28] [29] The midpoint of each side of the triangle; The foot ...
Given three points A, B and C on a circle with center O, the angle ∠ AOC is twice as large as the angle ∠ ABC. A related result to Thales's theorem is the following: If AC is a diameter of a circle, then: If B is inside the circle, then ∠ ABC > 90° If B is on the circle, then ∠ ABC = 90° If B is outside the circle, then ∠ ABC < 90°.
The incircle is the circle that lies inside the triangle and touches all three sides. Its radius is called the inradius. There are three other important circles, the excircles ; they lie outside the triangle and touch one side, as well as the extensions of the other two.
A polygon inscribed in a circle is said to be a cyclic polygon, and the circle is said to be its circumscribed circle or circumcircle. The inradius or filling radius of a given outer figure is the radius of the inscribed circle or sphere, if it exists.
Special angle-based triangles inscribed in a unit circle are handy for visualizing and remembering trigonometric functions of multiples of 30 and 45 degrees.. Angle-based special right triangles are specified by the relationships of the angles of which the triangle is composed.
A right triangle ABC with its right angle at C, hypotenuse c, and legs a and b,. A right triangle or right-angled triangle, sometimes called an orthogonal triangle or rectangular triangle, is a triangle in which two sides are perpendicular, forming a right angle (1 ⁄ 4 turn or 90 degrees).
Given a circle whose center is point O, choose three points V, C, D on the circle. Draw lines VC and VD: angle ∠DVC is an inscribed angle. Now draw line OV and extend it past point O so that it intersects the circle at point E. Angle ∠DVC intercepts arc DC on the circle. Suppose this arc includes point E within it.
In geometry, an isosceles triangle (/ aɪ ˈ s ɒ s ə l iː z /) is a triangle that has two sides of equal length or two angles of equal measure. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case.