Question

in circle m, diameters jl and hk each measure 16 centimeters. what is the approximate length of minor arc jh? round to the nearest tenth of a centimeter. 21.6 cm 3.5 cm 46.8 cm 6.9 cm

Explanation:

Step1: Find the radius of the circle

The diameter of the circle is \(d = 16\) cm. The radius \(r=\frac{d}{2}\), so \(r = 8\) cm.

Step2: Find the central angle of arc \(JH\)

Since \(JL\) and \(HK\) are diameters, \(\angle JMH=180^{\circ}- 25^{\circ}-90^{\circ}=130^{\circ}\) (assuming the vertical - angle and straight - angle properties. Wait, no, actually, since \(JL\) and \(HK\) are diameters, \(\angle JMH = 180-(90 + 25)=65^{\circ}\) (using the property that the sum of angles around a point on a straight - line is \(180^{\circ}\). The formula for the length of an arc is \(s=\frac{n\pi r}{180}\), where \(n\) is the central angle and \(r\) is the radius.
Substitute \(n = 65^{\circ}\) and \(r = 8\) into the formula: \(s=\frac{65\times\pi\times8}{180}\)

$$s=\frac{65\times3.14\times8}{180}=\frac{65\times25.12}{180}=\frac{1632.8}{180}\approx6.9$$

Answer:

\(6.9\) cm