SIMILAR TRIANGLES : Geometry  is  the  right  foundation  of all  painting,  I have  decided to  teach its  rudiments  and  principles  to  all  youngsters  eager for  art.   (Ans: r=2)

Example

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 6cm and 8 cm. Find the radius of the in circle.

Ans:    BC = 10cm

y + z = 8cm

x + z = 6cm

x + y = 10

⇒ x + y + z = 12

z = 12 - 10

z = 2 cm

∴radius = 2cm