(a) Using a ruler and a pair of compasses only, (i) construct \(\Delta\) XYZ such that |XY| = 8 cm and < YXZ = < ZYX = 45°. (ii) locate a point P inside the triangle equidistant from XY and XZ and also equidistance from YX and YZ. (iii) construct a circle touching the three sides of the triangle (iv) measure the radius of the circle.
(b) The length of the sides of a hexagon are x – 5, 2x, 2x, 2x + 7, 2x and 2x – 1. If the perimeter is 144 cm, find the value of x.
Explanation
(a) 
(b) \(x - 5 + 2x + 2x + 2x + 7 + 2x + 2x - 1 = 144\)
\(11x + 1 = 144\)
\(11x = 143\)
\(x = \frac{143}{11} = 13cm\)