1.

ABC is a right angle triangle,right angle at A.Acircle is inscribed in it.The length of two sides containing angle A is 12cm and 5cm find the radius

Answer»

The length of two SIDES CONTAINING angle A is 12cm and 5cm
So let AB = 12cm and AC = 5cm. BC is opposite to angle A, so BC is hypotenuse.
Using Pythagoras theorem,
BC² = AC² + AB²
⇒ BC² = 5² + 12²
⇒ BC² = 25+144
⇒ BC² = 169
⇒ BC = √169 = 13cm

Now from the centre of the circle O, draw perpendiculars to the three sides of the triangle. Note that OP=ON=OM = radius of circle = r. Now we can write that

Area of ΔABC = Area of ΔOAC + Area of ΔOAB + Area of ΔOBC
⇒ 0.5×AB×AC = 0.5×AC×ON + 0.5×AB×OP + 0.5×BC×OM
⇒ 0.5×12×5 = 0.5×( 5×r + 12×r + 13×r )
⇒ 12×5 = 5r + 12R + 13r
⇒ 60 = 30r
⇒ r = 60/30
⇒ r = 2cm

Thus the radius of the inscribed circle is 2cm.


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