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, ADꞱBC , BEꞱAC and CFꞱAB

We can say that ADꞱBC,

ABꞱCO and

ACꞱBO

So, A is the orthocenter of ΔOBC.

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