Question

Construct a ∆PQR in which QR = 6 cm, PQ = 4.4 cm and PR = 5.3 cm. Draw the bisector of ∠P.

Answer 1

$$\begin{gathered} \begin{array}{l}\text{Steps of construction:}\\ 1.\text{Draw a line segment QR of length 6 cm}\text{.}\\ \text{2}\text{. Draw arcs of 4}\text{.4 cm and 5}\text{.3 cm from Q and R, respectively. They intersect at P.}\\ \text{3}\text{. Draw an arc of any radius from the centre (P), cutting PQ and PR at S and T, respectively.}\\ \text{4}\text{. With S as the centre and the radius more than half of ST, draw an arc}\text{.}\\ \text{5. With T as the centre and the}\mathrm{same\; radius},draw\mathrm{another}\mathrm{arc}\mathrm{cutting}\mathrm{the}\mathrm{previously}\mathrm{drawn}\mathrm{arc}\mathrm{at}\mathrm{X}.\\ \text{6. Join P and X}\text{.}\end{array} \\ \mathrm{Then},\mathrm{PX}\mathrm{is}\mathrm{the}\mathrm{bisector}\mathrm{of}\angle \mathrm{P}. \end{gathered}$$