Isosceles Triangle Circumradius

In the KLM isosceles triangle, the KL base is 24 cm long, and the arm measures 15 cm. What is the radius of the circle described by this triangle?

Final Answer:

r =  12.5 cm

Step-by-step explanation:

$$\begin{gathered} m=24\text{cm} \\ k=15\text{cm} \\ l=k=15\text{cm} \\ x=m/2=24/2=12\text{cm} \\ \cos K=x/l \\ K=\frac{180°}{\pi }\cdot \arccos (x/l)=\frac{180°}{\pi }\cdot \arccos (12/15)\doteq 36.8699{}^{\circ } \\ r=\frac{k}{2\cdot \sin K}=\frac{k}{2\cdot \sin 36.869897645844°}=\frac{15}{2\cdot \sin 36.869897645844°}=\frac{15}{2\cdot 0.6}=12.5=\frac{25}{2}\text{cm}=12.5\text{cm} \end{gathered}$$

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