Question

The hypotenuse of a right angle triangle is 10 cm and radius of its inscribed circle is 1 cm. Therefore, perimeter of the triangle is :

Answer 1

With the given details, we can create a diagram.
Please refer to video for the diagram.
From the figure, incircle touches the circle at point `E,F and G`. Also, length of tangent from any common point outside a circle are always equal.
`:. GC = FC = 10-x`
`AE = AG =x`
`BE = BF =1`
Now, parameter of given triangle `ABC = AB+BC+AC`
`=AE+EB+BF+FC+AC`
`=x+1+1+10-x+10 = 22cm`
So, parameter of triangle `ABC` is `22` cm.