Question

Find the distance of point A from the circumcenter of a right angle triangle ABC with side AB = 20 cm, BC = 15 cm and ∠ABC = 90°.  
1. 25
2. 10
3. 7.5
4. 12.5

Answer 1

Correct Answer - Option 4 : 12.5

Given:

In triangle ABC,  AB = 20 cm, BC = 15 cm

Concept Used:

The circumcentre of a right angle triangle lies on the mid-point of the hypotenuse.

Formula Used:

Pythagoras theorem - In a Right angle triangle,

 Hypotenuse² = Perpendicular² + Base²

Calculation:

In ΔABC,

AC² = AB² + BC²

⇒ AC² = 20² + 15²

⇒ AC² = 625

⇒ AC = 25 cm

The distance of point A from the circumcentre = Circumradius of the triangle = 25/2 = 12.5 cm

∴ The distance of point A from the circumcentre is 12.5 cm