The Euler Area problem

If the coordinates of the centroid, orthocenter and circumcentre of a triangle are (0,a) ; (0,b) & (0,c) respectively, what is the area and perimeter of the triangle?

#Geometry

Easy Math Editor

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Comments

Nine point circle is relevant here.

Pi Han Goh - 4 years ago

Pls elaborate@Pi Han Goh

DIGVIJAY ROY VARIER - 4 years ago

How are the "centroid, orthocenter and circumcentre" are related to each other?

If we know that already, can we related "b" and "c" to "a" (and vice versa)? Can we actually solve for these values?

Pi Han Goh - 4 years ago

I also faced this same doubt..as far as i think..there can be more than one triangle..with different areas ..but having the same set of circumcentre orthocentre & centroid..am i right?@Pi Han Goh

DIGVIJAY ROY VARIER - 4 years ago

Instead of asking me questions, why don't you show your work and where you're stuck, so that I can identify where your issue is.

Pi Han Goh - 4 years ago

Ahmad Saad - 4 years ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$