ABC is a right-angled triangle right angled at A. A circle is inscribed in it the lengths of the two sides containing the right angle are 6 cm and 8 cm. Find the radius of the circle. [4 MARKS]
Concept: 1 Mark
Application: 1 Mark
Calculation : 2 Marks
Using Pythagoras theorem for ΔBAC, we have
BC2=AB2+AC2
⇒BC2=62+82=100⇒BC=10 cm
Now, Area of ΔABC=Area of ΔOAB+Area of ΔOBC+Area of ΔOCA
12AB×AC=12AB×r+12BC×r+12CA×r
12×6×8=12(6×r)+12(10×r)+12(8×r)
⇒24=3r+5r+4r
⇒24=12r
⇒r=2 cm