Radius of Circle Inscribed in Triangle II

Submitted by michaela.bailova on Tue, 08/20/2024 - 16:42

Project ID:

7300020131

Accepted:

SubArea:

Type:

Layout:

Question:

Match the triangle with the corresponding length of the radius

r

of its inscribed circle.

Hint: The radius

r

of the circle inscribed in a triangle is expressed by the formula:

r = \frac{P}{s}

where

P

is the area of the triangle and

s

is half the perimeter, i.e.,

s = \frac{1}{2} (a + b + c)

(see the picture). The area of a triangle can be found in terms of the lengths of its sides using Heron's formula:

P = \sqrt{s (s - a) (s - b) (s - c)}

Unfolding Image:

Questions Title:

Triangles:

Answers Title:

Radius of circle inscribed in triangle:

Question 1 Image:

Answer 1:

r = \frac{4}{3}

Question 2 Image:

Answer 2:

r = 6 - 3 \sqrt{2}

Question 3 Image:

Answer 3:

r = 4

Question 4 Image:

Answer 4:

r = 4 \sqrt{3} - 6

Answer 5:

$r = 8$

Answer 6:

r = 4 \sqrt{3} - 4

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