Q1 of 47 Page 1

In a right-angled triangle ABC, right angled at B, BC = 12 cm and AB = 5 cm. Calculate the radius of the circle inscribed in the triangle.


Given, BC = 12 cm, AB = 5 cm, ∠ABC = 90°


⇒ AC2 = AB2 + BC2 [By Pythagoras theorem]


⇒ AC2 = 52 + 122


⇒ AC = √169 = 13


⸫ Ar. (ΔABC) = Ar. (ΔAOB) + Ar. (ΔAOC) + Ar. (ΔBOC)


[Area of a right-angled triangle = × base × height]


⇒


[Tangent to a circle is perpendicular to the radius]


⇒ 30 × 2 = 5r + 13r + 12r


⇒ 30r = 60


⸫ r = 2 cm


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