Proof Images of orthocenter in any side of triangle lie on circumcircle

 Proof Images of orthocenter in any side of triangle lie on circumcircle

Proof of coordinates of orthocenter of triangle

 Proof of coordinates of orthocenter of triangle

Proof of coordinates of circumcenter of triangle

 Proof of coordinates of circumcenter of triangle

Proof of coordinates of excenter

 

Proof of coordinates of Incenter

 Coordinates of Incenter

To know the proof of BD:DC::c:b visit following link

https://maths49.blogspot.com/2022/01/angle-bisector-divides-opposite-side-in.html

Or 

https://maths49.blogspot.com/2022/01/internal-angle-bisector-divides.html

To know the proof of AI:ID::b+c:a visit following link

https://maths49.blogspot.com/2022/01/proof-of-incenter-divides-internal.html

Proof of Incenter divides the internal angle bisector in the ratio of b+c:a

 Incenter of triangle divides the internal angle bisector in ratio of b+c:a

For proof of BD:CD::c:b visit following links

https://maths49.blogspot.com/2022/01/angle-bisector-divides-opposite-side-in.html

Or 

https://maths49.blogspot.com/2022/01/internal-angle-bisector-divides.html

Internal angle bisector divides the opposite side internally of triangle in the ratio of the corresponding sides containing the angle.

Internal angle bisector of angle of triangle divides the opposite side internally of triangle in the ratio of the corresponding sides containing the angle.

For alternate method open this link

https://maths49.blogspot.com/2022/01/angle-bisector-divides-opposite-side-in.html

Angle bisector divides the opposite side in the ratio of sides of triangle

The Internal angle bisector of an angle of a triangle divides the opposite side internally in the ratio of the corresponding sides containing the angle

For short method visit this link

https://maths49.blogspot.com/2022/01/internal-angle-bisector-divides.html

 

Formula Centroid of triangle with proof and key points

 

 

Parametric equation of straight line

 

Angle between two lines formula with proof and key points

 

Proof of formula of area of polygon

 

Proof of area of triangle

 

Harmonic conjugate

 

Proof of external division formula

 

Proof internal division

 

Proof of distance formula