How do you find the area of triangle ABC?

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How do you find the area of triangle ABC?

Since triangle ABC has a right angle, we now use the internal angle (to the triangle) A to write. The area At might also be written as follows (using the identity sin (2A) = 2 sin (A) cos (A)). The above equation gives.

How do you find the circumscribed circle of a triangle?

For the circumscribed circle of a triangle, you need the perpendicular bisectors of only two of the sides; their intersection will be the center of the circle. Example 2. Find the radius R of the circumscribed circle for the triangle △ABC where a = 2, b = 3, and c = 4. Then draw the triangle and the circle.

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How do you find the area of an inscribed circle?

The segments from the incenter to each vertex bisects each angle. The distances from the incenter to each side are equal to the inscribed circle’s radius. The area of the triangle is equal to 21 ×r×(the triangle’s perimeter), where r is the inscribed circle’s radius.

How do you find the angles of a circle?

To calculate the angles within circles using trigonometric functions, triangle properties, and given circle properties. This common ratio has a geometric meaning: it is the diameter (i.e. twice the radius) of the unique circle in which △ ABC can be inscribed, called the circumscribed circle of the triangle.

What is the orthic triangle of ABC?

The orthic triangleof ABC is defined to be A*B*C*. Thistriangle has some remarkable properties that we shall prove: The altitudes and sides of ABC are interior and exterior angle bisectors of orthic triangle A*B*C*, so H is the incenter of A*B*C* and A, B, C are the 3 ecenters (centers of escribed circles).

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What is the circum circle of ABC?

The triangle ABC can be inscribed in a circle called thecircumcircle of ABC. There aresome remarkable relationships between the orthocenter H and the circumcircle. The altitude line CC* intersects the circumcircle in twopoints. One is C. Denote the other one by C**. Proposition. The point CC* is the reflection of H inline AB.

What are the altitudes of the sides of ABC?

The altitudes and sides of ABC are interior and exterior angle bisectors of orthic triangle A*B*C*, so H is the incenter of A*B*C* and A, B, C are the 3 ecenters (centers of escribed circles). The sides of the orthic triangle form an “optical” or “billiard” pathreflecting off the sides of ABC.

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