Of all the lines segments drawn from a point `P` to a line `m` not containing `P ,` let `P D` be the shortest. If `B\ a n d\ C` are points on `m` such that `D` is the mid-point of `B C` , prove that `P B=P C` .

Of all the line segments drawn from a point P to a line m not containing P , let P D be the shortest. If B and C are points on m such that D is the mid-point of B C , prove that P B=P Cdot

In Figure, A B C D\ a n d\ P Q R C are rectangles and Q is the mid-point of A C . Prove that D P=P C (ii) P R=1/2\ A C

In Figure, if A B||D C\ a n d\ P is the mid-point B D , prove that P is also the midpoint of A C

Of all the line segments that can be drawn to a given line, from a point, not lying on it, the perpendicular line segment is the shortest. GIVEN : A straight line l and a point P not lying on ldot P M_|_l and N is any point on 1 other than Mdot TO PROVE : P M

In Figure, line segments A B is parallel to another line segment C D .O is the mid-point of A D . Show that: A O B~=\ \ D O C .

In figure, P is the mid-point of B C , ,Q is the mid-point of A P , such that B Q produced meets A C at Rdot Prove that 3RA= CA

In Figure, line segments A B is parallel to another line segment C DdotO is the mid-point of A Ddot Show that: O is also the mid-point of B D

In a triangle A B C , let P and Q be points on AB and AC respectively such that P Q || B C . Prove that the median A D bisects P Q .

In the figure, BX bisects angle ABC and intersects AC at point D. Line segment CY is perpendicular to AB and intersects BX at point P. If Y is mid-point of AB, prove that : point P is equidistant from A and B.

In Figure, P , is any point on the chord B C of a circle such that A B=A P . Prove that C P=C Q .