Question

point x is the circumcenter of \\( \triangle abc \\).
what is the length of xb?
4.2 cm
4.6 cm
4.8 cm

Explanation:

Step1: Use the Pythagorean theorem

In right - triangle \(XMB\), we know that \(XM = 3.2\mathrm{cm}\) (the perpendicular distance from the circum - center to the side, since \(X\) is the circum - center and \(XM\perp AB\)), \(BM=2.3\mathrm{cm}\) (half of the side \(AB\) as the circum - center's perpendicular to a side bisects the side). According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a = BM\), \(b = XM\), and \(c = XB\).

$$XB=\sqrt{BM^{2}+XM^{2}}$$

Step2: Substitute the values

Substitute \(BM = 2.3\) and \(XM = 3.2\) into the formula:

$$XB=\sqrt{(2.3)^{2}+(3.2)^{2}}=\sqrt{5.29 + 10.24}=\sqrt{15.53}\approx 4.8\mathrm{cm}$$

Answer:

\(4.8\mathrm{cm}\)