Question

In the given figure, \(\triangle ABC\) is a right triangle in which \(\angle B = 90^\circ\), \(AB = 4\) cm and \(BC = 3\) cm. Find the radius of the circle inscribed in the triangle ABC.

Hint:

For any triangle, the area can also be expressed as \(Area = r \times s\), where \(r\) is inradius and \(s\) is semi-perimeter. This is another great way to find the radius!

Answer 1

Step 1: Understanding the Concept:
In a right-angled triangle, the radius of the incircle (inradius) can be calculated using the sides of the triangle.
For a right triangle, the inradius formula is:
r = (Sum of perpendicular sides − Hypotenuse) / 2

Step 2: Given Information:
AB = 4 cm
BC = 3 cm

Since AB and BC are perpendicular sides, we first find the hypotenuse AC using Pythagoras theorem.

Step 3: Finding the Hypotenuse:
AC² = AB² + BC²
= 4² + 3²
= 16 + 9
= 25

AC = √25
AC = 5 cm

Step 4: Applying Inradius Formula:
r = (AB + BC − AC) / 2
= (4 + 3 − 5) / 2
= 2 / 2
= 1 cm

Final Answer:
The radius of the inscribed circle is 1 cm.