A circle is inscribed in a triangle. What is the relationship between the radius

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Question: A circle is inscribed in a triangle. What is the relationship between the radius of the incircle and the area of the triangle?

Options:

Correct Answer: r = A/s

Solution:

The radius of the incircle (r) is given by the formula r = A/s, where A is the area of the triangle and s is the semi-perimeter.

A circle is inscribed in a triangle. What is the relationship between the radius of the incircle and the area of the triangle?

A circle is inscribed in a triangle. What is the relationship between the radius of the incircle and the area of the triangle?

Step 1: Understand that a triangle can have a circle inside it, called the incircle.
Step 2: The radius of this incircle is denoted as 'r'.
Step 3: The area of the triangle is denoted as 'A'.
Step 4: The semi-perimeter of the triangle is denoted as 's', which is half of the perimeter.
Step 5: The relationship between the radius of the incircle and the area of the triangle is given by the formula: r = A/s.
Step 6: This means that if you know the area of the triangle and its semi-perimeter, you can find the radius of the incircle.

Incircle and Triangle Area Relationship – The relationship between the radius of the incircle (r) and the area (A) of a triangle, expressed through the formula r = A/s, where s is the semi-perimeter.
Semi-perimeter – Understanding the semi-perimeter (s) as half the sum of the triangle's side lengths, which is crucial for applying the incircle radius formula.