# CAT Practice : Coordinate Geometry

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Very simple Question! Find out what type of triangle it is, locate its orthocenter and circumcenter!

## Distance between orthocenter and circumcenter

Q.29: What is the distance between the orthocentre and the circumcenter of a triangle who sides measure 24 cm, 26 cm and 10 cm?
1. 13 cm
2. 12 cm
3. 7.5 cm
4. ${\surd 30}$ cm

Choice (A). 13 cm

## Detailed Solution

The sides measure 24 cm, 26 cm and 10 cm. 10, 24, 26 is a Pythagorean triple!

So it is a right angled triangle we are talking about.

Draw the perpendicular bisectors to get the circumcenter. Orthocenter is the point where all altitudes meet. In a right angled triangle it is the vertex that makes 90 deg angle.

Now it is easy to find OC! It is the length of the diagonal of the rectangle formed.

Length = 12 cm, breadth = 5 cm

Diagonal = ${\surd (12 ^2 + 5 ^ 2)}$ = 13

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Geometry is probably the most vital topic as far as CAT preparation is concerned. Geometry sets the stage for Trigonometry, Cogeo and Mensuration as well.