the cordinates of the feet of perpendiculars from the vertices of a triangle on the opposite sides are (20,25), (8,16), (8,9) so the coordinates of a vertexof the triangle are

we take a triangle ABC and draw 3 perpendiculars from the three vertices we get AL ,BM,CN

now we have a concept that the triange formed by the points LMN is a pedal triangle and the orthocentre of ABC triangle =the incentre of triangle LMN so finding the incentre of triangle LMN we get the point (10,15) which is also the orthocentre of tringle ABC

note: for the incentre i used the formulae  (lx₁ + mx₂ + nx₃)/l+m+n and similarly for the y coordinate

now slope of AL is -1/2 and as AL is perpendicular to BC so slope of BC is 2 similarly for other two sides we get the slope of AB=-1/3  and slope of AC is -1 so now using these points we have

equation of AB ---------->   3y+x=35

equation of AC ---------->  x+y=45

equation of BC ---------->  y=2x

now AB equation satisfies option A,B

AC equation satisfies option B,C

BC equation satisfies option A,C