Question

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example 4

1. mp sense-making if q is the incenter of $\triangle jln$, find $jq$.

Explanation:

Step1: Identify right triangle JQP

We know Q is the incenter, so QP = 9 (inradius, perpendicular to side JN). Side JP = 16.5, and △JQP is a right triangle with right angle at P.

Step2: Apply Pythagorean theorem

Use $c^2 = a^2 + b^2$ to find JQ, where $a=16.5$, $b=9$.
$$JQ = \sqrt{JP^2 + QP^2} = \sqrt{16.5^2 + 9^2}$$

Step3: Calculate squared terms

Compute $16.5^2 = 272.25$ and $9^2 = 81$.
$$272.25 + 81 = 353.25$$

Step4: Compute square root

Calculate the square root of 353.25.
$$\sqrt{353.25} = 18.795 \approx 18.8$$
Or as an exact value: $\sqrt{\frac{1413}{4}} = \frac{3\sqrt{157}}{2}$

Answer:

$\frac{3\sqrt{157}}{2}$ (or approximately 18.8)