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# Geometry

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In triangle JKL, we have JK = JL = 25 and KL = $$10$$. Find the circumradius

Apr 16, 2022

#1
+9459
+1

We calculate the area of the triangle.

Area of triangle JKL = $$\dfrac12 \cdot 10 \cdot \sqrt{25^2 - \left(\dfrac{10}2\right)^2} = 50\sqrt 6$$

Then, we use the formula $$\text{circumradius} = \dfrac{\text{product of 3 sides}}{4(\text{area})}$$

$$\text{circumradius} = \dfrac{25(25)(10)}{4(50\sqrt 6)} = \dfrac{125}{24}\sqrt6$$

Wolfram alpha output

Apr 16, 2022

#1
+9459
+1

We calculate the area of the triangle.

Area of triangle JKL = $$\dfrac12 \cdot 10 \cdot \sqrt{25^2 - \left(\dfrac{10}2\right)^2} = 50\sqrt 6$$

Then, we use the formula $$\text{circumradius} = \dfrac{\text{product of 3 sides}}{4(\text{area})}$$

$$\text{circumradius} = \dfrac{25(25)(10)}{4(50\sqrt 6)} = \dfrac{125}{24}\sqrt6$$

Wolfram alpha output

MaxWong Apr 16, 2022