LINGKARAN DALAM SEGITIGA DAN LINGKARAN LUAR SEGITIGA

Summary

This video discusses the concepts of the incircle and circumcircle within a triangle. The incircle is a circle inscribed inside the triangle, tangent to all three sides, while the circumcircle is a circle passing through all the triangle’s vertices. The script explains how to calculate the radius of both circles using mathematical formulas, incorporating the semi-perimeter and area of the triangle. Examples with right triangles are used to demonstrate how to apply the formulas, ultimately leading to the calculation of the ratio between the radii of the incircle and circumcircle.

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Q & A

What is the incircle of a triangle?

The incircle of a triangle is a circle that is inscribed within the triangle, with its sides acting as tangents to the circle. The center of this circle is the incenter, which is equidistant from all three sides of the triangle.

How do we calculate the radius of the incircle of a triangle?

The radius (r) of the incircle can be calculated using the formula r = A / s, where A is the area of the triangle and s is the semi-perimeter (half of the perimeter) of the triangle.

What is the circumcircle of a triangle?

The circumcircle of a triangle is a circle that passes through all three vertices of the triangle. The center of the circumcircle is the circumcenter, and the radius is called the circumradius.

How do we calculate the radius of the circumcircle of a triangle?

The radius (R) of the circumcircle is calculated using the formula R = (a * b * c) / (4 * A), where a, b, and c are the sides of the triangle, and A is the area of the triangle.

How do we find the semi-perimeter (s) of a triangle?

The semi-perimeter (s) of a triangle is calculated as s = (a + b + c) / 2, where a, b, and c are the lengths of the sides of the triangle.

What formula is used to find the area of a triangle when the lengths of the sides are known?

When the lengths of the sides (a, b, and c) of a triangle are known, the area (A) can be calculated using Heron's formula: A = √[s(s - a)(s - b)(s - c)], where s is the semi-perimeter of the triangle.

In a right-angled triangle, how do you find the third side if two sides are known?

In a right-angled triangle, the third side can be found using the Pythagorean theorem. If the lengths of the two legs are known (a and b), the hypotenuse (c) is found using c = √(a² + b²). If the hypotenuse and one leg are known, the other leg can be found using a = √(c² - b²) or b = √(c² - a²).

How can the area of a triangle be expressed using its sides and semi-perimeter?

The area of a triangle can be expressed using Heron's formula as A = √[s(s - a)(s - b)(s - c)], where s is the semi-perimeter and a, b, and c are the lengths of the triangle's sides.

What is the relationship between the circumradius and the incircle radius?

The circumradius (R) and the incircle radius (r) are related geometrically, but there isn't a simple direct formula to express one in terms of the other. However, for a given triangle, they can be calculated independently using their respective formulas based on the sides and area of the triangle.