From a point O inside a triangle ABC, perpendiculars OD, OE and OF are drawn to the sides BC, CA and AB, respectively. Prove that the perpendiculars from A, B and C to the sides EF, FD and DE are concurrent

From a point O inside a triangle ABC , perpendiculars OD,OE and Of are drawn to rthe sides BC,CA and AB, respecrtively. Prove that the perpendiculars from A,B, and C to the sides EF, FD and DE are concurrent.

From a point O inside a triangle A B C , perpendiculars O D ,O Ea n dOf are drawn to rthe sides B C ,C Aa n dA B , respecrtively. Prove that the perpendiculars from A ,B ,a n dC to the sides E F ,F Da n dD E are concurrent.

In Delta ABC, AB = AC. D , E and F are mid-points of the sides BC, CA and AB respectively . Show that : AD is perpendicular to EF.

Prove that the perpendicular bisectors of the sides of triangle are concurrent.

Prove analytically : The perpendicular bisector of the sides of a triangle are concurrent.

In Delta ABC, AD and BE are perpendiculars from A and B to the sides BC and AC, then

A, B and C are three points on a circle. Prove that the perpendicular bisectors of AB, BC and CA are concurrent.

If P,Q and R are the mid-point of the side BC,CA and AB of a triangle and AD is the perpendicular form A and BC, prove that P,Q and D are concylic.