Question

circle centered at o. given that wy = 14.4 and ow = 19.4, find ox. ox =

Explanation:

Step1: Find the length of \( WX \)

Since the perpendicular from the center of a circle to a chord bisects the chord. If \( OY \perp WX \), then \( WX=\frac{WY}{2}\). Given \( WY = 14.4\), so \( WX=\frac{14.4}{2}=7.2\).

Step2: Use the Pythagorean theorem

In right - triangle \( O W X\), by the Pythagorean theorem \(OX=\sqrt{OW^{2}-WX^{2}}\). Given \(OW = 19.4\) and \(WX = 7.2\), then \(OX=\sqrt{19.4^{2}-7.2^{2}}=\sqrt{(19.4 + 7.2)(19.4-7.2)}=\sqrt{26.6\times12.2}=\sqrt{324.52}\approx18.0\)

Answer:

\(18.0\)