Co-ordinate Geometry - radical center

1

this is a really easy problem

at the orthocentre

just go to the basics of radical centre (intersection of racical axes)

and apply a bit geometry

24

show me the solution..........................

1

ok

see the figure

BP is one of those radical axes

As BP is common to bothe the circles

and BPC and APB both are semicircles

hence we get

âˆšAPB=90

and
âˆšBPC=90

hence âˆšAPC=90+90=180

hence APC is a straight line

but there exists only one straight line between A and C

(the side AC)

hence BP is perpendicular to AC

thuse each radical axis is an altitude

hence the radical centre is the meeting point of the altitudes i.e circumcentre

radical center