Incenter & Circumcenter Review

Front

What is the incenter of a triangle?

Back

The incenter of a triangle is the point where the three angle bisectors intersect, and it is also the center of the circle inscribed within the triangle.

Front

What is the circumcenter of a triangle?

Back

The circumcenter of a triangle is the point where the three perpendicular bisectors of the sides intersect, and it is the center of the circle that passes through all three vertices of the triangle.

Front

What theorem is used to find the length of a side in a right triangle?

Back

The Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Front

If P is the incenter of triangle JKL, what can be inferred about the distances from P to the sides of the triangle?

Back

The distances from the incenter P to each side of triangle JKL are equal.

Front

In triangle ABC, if D is the midpoint of side AB, what is the relationship between AD and DB?

Back

AD is equal to DB, as D is the midpoint.

Front

What is the relationship between the circumcenter and the vertices of a triangle?

Back

The circumcenter is equidistant from all three vertices of the triangle.

Front

How do you find the circumradius of a triangle?

Back

The circumradius (R) can be found using the formula R = (abc) / (4K), where a, b, and c are the lengths of the sides of the triangle and K is the area of the triangle.

Front

What type of triangle has its circumcenter located outside the triangle?

Back

An obtuse triangle has its circumcenter located outside the triangle.

Front

What is the significance of the inradius in a triangle?

Back

The inradius is the radius of the inscribed circle, which is tangent to each side of the triangle.

Front

If a triangle has sides of lengths 3, 4, and 5, what type of triangle is it?

Back

It is a right triangle, as it satisfies the Pythagorean theorem (3^2 + 4^2 = 5^2).