Q. 64.1( 7 Votes )

The orthocenter of ΔABC is P. Prove that the orthocenter of ΔABC is the point A.

Answer :

Given that P is the orthocenter of ΔOBC.

To prove: the orthocenter of ΔABC is the point A


Proof:



P is the orthocenter of ΔABC


As we know that orthocenter is the point of all the perpendicular bisectors of the sides of a triangle.


Let AO is extended to D , BO is extended to E and CO is extended to F respectively.


So, AD=AO+OD


BE=BO+OE


And CF=CO+OF


As AD, BE and CF are the perpendicular bisectors


So, ADBC , BEAC and CFAB


We can say that ADBC,


ABCO and


ACBO


So, A is the orthocenter of ΔOBC.


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