Question

Point x is the circumcenter of triangle ABC

What is the length of XB?

4.2 cm
4.6 cm
4.8 cm
5.3 cm

Answer 1

The answer is 5.3 cm.

Answer 2

XB ≈ 5.3 cm

Explanation:

From the diagram :

In ΔXNC,

m∠XNC = 90°

Now, m∠XNC + m∠XNB = 180° ( Sum of angles forming a linear pair is supplementary )

⇒ 90° + m∠XNB = 180°

⇒ m∠XNB = 180° - 90°

⇒ m∠XNB = 90°

Now, in right angled ΔXNB Applying Pythagoras theorem , We have

XB² = NB² + XN²

⇒ XB² = 4.2² + 3.2²

⇒ XB² = 27.88

⇒ XB = 5.28 cm

⇒ XB ≈ 5.3 cm