Construction of a Triangle with 3 given sides

1. Draw a triangle \(ABC\) to scale where \(AB\mathrm{ }=\mathrm{ }12\) cm, \(AC\mathrm{ }=\mathrm{ }8.5\) cm and \(BC\mathrm{ }=\mathrm{ }7\) cm.
2. By drawing suitable lines, locate a point \(P\) such that \(P\) is equidistant from line \(AB\), line \(BC\), point \(A\) and point \(B\).

Interpret part (b) as two separate conditions: \(PA=PB\), and the perpendicular distances from \(P\) to the lines \(AB\) and \(BC\) are equal. The point-to-point distance need not equal the point-to-line distance. Requiring all four distances to be identical would have no solution.