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# pls help. im desperate.

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What is the radius of the circle inscribed in triangle ABC if AB = AC=7 and BC=6? Express your answer in simplest radical form.

Aug 2, 2022

#1
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The inradius is $$\text{Area} \over \text{semiperimeter}$$

By Heron's formula, the area is $$\sqrt{s(s-a)(s-b)(s-c)} = \sqrt{10 \times 3 \times 3 \times \times 4} = \sqrt{360} = \sqrt{36} \times \sqrt {10} = 6 \sqrt{10}$$

The semiperimeter is $$(7 + 7 + 6) \div 2 = 10$$, so the inradius is $${6 \sqrt{10} \over 10} = \color{brown}\boxed{3 \sqrt {10} \over 5}$$

Aug 2, 2022

#1
+1

The inradius is $$\text{Area} \over \text{semiperimeter}$$

By Heron's formula, the area is $$\sqrt{s(s-a)(s-b)(s-c)} = \sqrt{10 \times 3 \times 3 \times \times 4} = \sqrt{360} = \sqrt{36} \times \sqrt {10} = 6 \sqrt{10}$$

The semiperimeter is $$(7 + 7 + 6) \div 2 = 10$$, so the inradius is $${6 \sqrt{10} \over 10} = \color{brown}\boxed{3 \sqrt {10} \over 5}$$

BuilderBoi Aug 2, 2022
#2
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thank you!!! it was correct btw. :))

Guest Aug 2, 2022