# Finding radius of circle inscribed in a triangle

• Bohrok
In summary, the conversation discusses a problem involving finding the radius of a circle inscribed in a triangle. The person asking the question tried solving it using basic algebra but was unable to make progress. They wonder if the problem can be solved using basic algebra or geometry and if it would be easier if the triangle was a right triangle. The responder suggests using circle theorems and trigonometry, and mentions that the two tangents made by the given lines are equal according to a circle theorem.
Bohrok

## Homework Statement

Someone gave me this problem: finding the radius of the circle inscribed in the triangle with the given lengths.

## The Attempt at a Solution

The person asking about this problem said it was taken from a beginning algebra textbook. I tried figuring it out using just basic algebra, but I couldn't make any progress. Is this problem solvable with basic algebra/geometry? Would it be any easier if it were a right triangle?

What I can deduce that you must use are some of the circle theorems, such as the angle made by a tangent and radius at the point of contact is 90°, as well as possibly some trigonometry.

I believe that the two tangents that meet (made by the 4 unit and 3 unit line) are both equal by one of the circle theorems.

## 1. What is the formula for finding the radius of a circle inscribed in a triangle?

The formula for finding the radius of a circle inscribed in a triangle is r = (abc)/(4A), where a, b, and c are the sides of the triangle and A is the area of the triangle.

## 2. Can the radius of a circle inscribed in a triangle be greater than or equal to the length of any side of the triangle?

No, the radius of a circle inscribed in a triangle can never be greater than or equal to the length of any side of the triangle. It will always be less than the length of the shortest side of the triangle.

## 3. How do I find the area of a triangle if the radius of the inscribed circle is given?

The area of a triangle can be found by using the formula A = rs, where r is the radius of the inscribed circle and s is the semi-perimeter of the triangle (s = (a+b+c)/2).

## 4. Is the radius of a circle inscribed in a right triangle always equal to half the length of the hypotenuse?

Yes, the radius of a circle inscribed in a right triangle is always equal to half the length of the hypotenuse. This is a special case of the general formula mentioned above, where the area of the triangle becomes A = (1/2)(ab).

## 5. Can the radius of a circle inscribed in an equilateral triangle be calculated without knowing the length of its sides?

Yes, the radius of a circle inscribed in an equilateral triangle can be calculated without knowing the length of its sides. It is equal to (2/3) times the height of the triangle, or (2/3)(√3/2)a, where a is the length of any side of the triangle.

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