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Question

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]


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Solution

Concept: 1 Mark
Application: 1 Mark
Calculation : 2 Marks

Using Pythagoras theorem for ΔBAC, we have

BC2=AB2+AC2

BC2=62+82=100BC=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


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