(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)