Question

Draw any angle with vertex O. Take a point A on one of its arms and B on another such that OA = OB. Draw the perpendicular bisectors of `overline"OA"` and `overline"OB"`. Let them meet at P. Is PA = PB ?

Answer 1

1. Draw any angle whose vertex is O.
   
2. With a convenient radius, draw arcs on both rays of this angle while taking O as centre. Let these points be A and B.
   
3. Taking O and A as centres and with radius more than half of OA, draw arcs on both sides of OA. Let these be intersecting at C and D. Join CD.
   

4. Similarly, we can find the perpendicular bisector `overline"EF"` of `overline"OB"`. These perpendicular bisectors `overline"CD"` and `overline"EF"` will intersect each other at P.

   Now, PA and PB can be measured. These are equal in length.