Town 𝑀 is 20 𝑘𝑚 from town 𝑁 and 22 𝑘𝑚 from town 𝑃 while 𝑁 is 18 𝑘𝑚 from 𝑃. A market is to be
built to serve the three towns. It is to be located such that traders from 𝑁 and 𝑀 will always travel equal
distance to access the market while trades from 𝑃 will travel exactly 10 𝑘𝑚 to reach the market.
a. Using a ruler and pair of compasses only, find by construction, the possible locations for the market.
Use a scale of 1 𝑐𝑚 to 2 𝑘𝑚.
b. How many such locations are there?
c. Measure and record the distances of the locations from town 𝑁.
d. Which of all the locations would be convenient for all three towns?