Question

By using ruler and compass only, construct an isosceles triangle ABC in which BC = 5 cm, AB = AC and ∠BAC = 90°. Locate the point P such that 

1. P is equidistant from the sides BC and AC. 
2. P is equidistant from the point B and C.

Answer 1

1. • Draw BC = 5 cm.
   • Draw the perpendicular bisector of BC.
   • Draw a semicircle on BC as a diameter.
   • The perpendicular bisector meets the semicircle at A.
     Join A to B and A to C. Triangle ABC is isosceles with AB = AC and ∠BAC = 90°.
2. • Construct the bisector of ∠BCA (sides BC and AC).
   • Draw the perpendicular bisector of BC.

Their intersection gives point P.