Question

In the given figure, Δ ABC is a right triangle in which ∠ B = 90°, AB = 4 cm and BC = 3 cm. Find the radius of the circle inscribed in the triangle ABC.

Answer 1

In the right-angled Δ ABC, use the Pythagoras theorem to find the length of side AC:

AC² = AB² + BC²

AC² = 4² + 3²

AC² = 16 + 9

AC = `sqrt25`

= 5 cm

For a right-angled triangle, the radius r of the inscribed circle is given by:

r = `(AB + BC - AC)/2`

= `(4 + 3 - 5)/2`

= `(7 - 5)/2`

= `2/2`

= 1 cm

Area of a triangle = `1/2 xx "base" xx "height"`

= `1/2 xx 3 xx 4`

= `12/2`

= 6 cm