Question

1. find $jn$ if $m$ is the circumcenter of $\triangle jlq$, $mn = 5.6$, and $mq = 8.7$. round to the nearest tenth.
2. find $jk$ if $m$ is the circumcenter of $\triangle jlq$, $ml = 8.7$, and $km = 1.8$. round to the nearest tenth.

Explanation:

For Question 10:

Step1: Identify circumcenter property

As \(M\) is the circumcenter of \(\triangle JLQ\), \(MJ = MQ = 8.7\) (circumradius).

Step2: Use Pythagorean theorem

In right \(\triangle JNM\), solve for \(JN\):
$$JN = \sqrt{MJ^2 - MN^2}$$
Substitute \(MJ=8.7\), \(MN=5.6\):
$$JN = \sqrt{8.7^2 - 5.6^2} = \sqrt{75.69 - 31.36} = \sqrt{44.33}$$

Step3: Calculate and round

$$\sqrt{44.33} \approx 6.7$$

Step1: Identify circumcenter property

As \(M\) is the circumcenter of \(\triangle JLQ\), \(MJ = ML = 8.7\) (circumradius).

Step2: Use Pythagorean theorem

In right \(\triangle JKM\), solve for \(JK\):
$$JK = \sqrt{MJ^2 - KM^2}$$
Substitute \(MJ=8.7\), \(KM=1.8\):
$$JK = \sqrt{8.7^2 - 1.8^2} = \sqrt{75.69 - 3.24} = \sqrt{72.45}$$

Step3: Calculate and round

$$\sqrt{72.45} \approx 8.5$$

Answer:

\(6.7\)

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For Question 11: