What do the orthocenter, centroid, and circumcenter share in common? They lie on the Euler line! See more
At the 1920 FIFA World Cup, there was an earth quake during one of the games and a hole was created with a diameter of 4 feet and sloping sides both 4 feet long from ground-level to the bottom of the pit. The soccer ball, with a radius of one foot, fell into the hole. Find the distance from the center of the Soccer ball to the bottom of the pit in feet.
- The sides of the hole are perfectly straight and smooth.
- The ball falls as far as it can with out changing shape.
- FYI, there wasn't actually an earthquake at the 1920 FIFA World Cup.
Note: Diagram is not drawn to scale.
Consider the isoscles \(\Delta ABC\) where \(AB=AC=5 \ , \ BC=6\) and denote \(I,O,H\) are its incenter, circumcenter, orthocenter respectively. Find the area of \(\Delta IOH\).