1. On a new page, draw a triangle ABC with the lengths of its sides a = 6 cm, b = 5 cm and c = 4 cm such that BC is the (horizontal) base, with the vertex B at (approximate) distances of 11 cm from the top of your page and 7 cm from the left margin. (Use another separately new page for the calculations involved.)
(i) Draw the three internal angle bisectors of ABC by using a compass, pencil and ruler. Discuss why these bisectors are concurrent at the incentre, I, of ABC.
(ii) Draw the incircle of ABC.
(iii) Prove that the altitude of ABC from A to BC equals $5\sqrt{7}/4$ cm. Hence find the area of ABC.
(iv) Find the areas of the triangles IAB, IBC and ICA in terms of r, the inradius of ABC. Hence, use your answer in (iii) to calculate the value of r.
(v) Draw the three external angle bisectors of ABC by using a compass, pencil and ruler. Discuss why any two of these bisectors are concurrent with the internal bisector on the other angle. [Hint: Use the equidistance of the angle bisector from the two lines that form the angle.]
(vi) Draw the three excircles of the triangle ABC. Hence, discuss the accuracy of all your drawings.
