Question

point x is the circumcenter of δabc.
what is the length of mb?
○ 1.5 cm
○ 2 cm
○ 2.5 cm
○ 3 cm
(diagram: triangle abc with circumcenter x, right angles at m (on ab), l (on ac), n (on bc); lengths: am=2.5 cm, al=3 cm, xb=3 cm, bn=2 cm)

Explanation:

Step1: Recall circumcenter property

The circumcenter of a triangle is the point where the perpendicular bisectors of the sides intersect. So, \(XM\) is the perpendicular bisector of \(AB\), meaning \(M\) is the midpoint of \(AB\), and \(AM = MB\).

Step2: Identify \(AM\) length

From the diagram, \(AM = 2.5\) cm.

Step3: Determine \(MB\) length

Since \(M\) is the midpoint, \(MB=AM = 2.5\) cm.

Answer:

\(2.5\) cm (corresponding to the option "2.5 cm")