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Question

ABC is a right triangle, right angled at B. 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 incircle. [4 MARKS]

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Solution

Concept: 1 Mark
Application: 3 Marks

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Let the radius of the incircle be x cm.

Let the incircle touch the side AB, BC and CA at D, E, F respectively.

Let O be the centre of the circle.

Then, OD = OE = OF = x cm.

Also, AB = 8 cm and BC = 6 cm.

Since the tangents to a circle from an external point are equal, we have

AF = AD = (8 – x) cm, and

CF = CE = (6 – x) cm.

Therefore, AC = AF + CF = (8 – x) cm + (6 – x) cm

= (14 – 2x) cm.

AC2=AB2+BC2

(142x)2=82+62=100=(10)2

142x=±10x=2 or x=12

x=2 [neglecting x = 12].

Hence, the radius of the incircle is 2cm.


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