Question

(vi) In a triangle ABC, ABC = 90°, AB = 5 cm, BC = 12 cm, Find the length of the circumradius of triangle ABC?
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Answer 1

Answer:

Length of Circumradius = 6.5 cm

Step-by-step explanation:

This triangle is right-angled. Its 3rd side can be found using the Pythagorean theorem:-

$AC = \sqrt{(AB)^{2}+(BC)^{2}} \\ \\ \\AC = \sqrt{(5^{2}+(12)^{2}} \\ \\ \\AC = \sqrt{(25+144)} \\ \\ \\AC = \sqrt{(169)} \\ \\ \\AC = 13 \ cm$

The circumradius for any triangle can be found using the formula:-

$R = \dfrac{abc}{\sqrt{(a+b+c)(a+b-c)(b+c-a)(a+c-b)}} \\ \\ \\R = \dfrac{5 \times 12 \times 13}{\sqrt{(5+12+13)(5+12-13)(12+13-5)(5+13-12)}} \\ \\ \\R = \dfrac{780}{\sqrt{30 \times 4 \times 20 \times 6}} \\ \\ \\R = \dfrac{780}{\sqrt{14400}} \\ \\ \\R = \dfrac{780}{120} \\ \\ \\R = 6.5 \ cm$