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(C) Given: The lengths of the sides of a triangle are $a = 15$,$b = 20$,and $c = 25$ units.First,observe that $15^2 + 20^2 = 225 + 400 = 625 = 25^2$.S

Vedclass · Accepted Answer

$12.5$

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(C) Given: The lengths of the sides of a triangle are $a = 15$,$b = 20$,and $c = 25$ units.First,observe that $15^2 + 20^2 = 225 + 400 = 625 = 25^2$.Since $a^2 + b^2 = c^2$,the triangle is a right-angled triangle with the hypotenuse $c = 25$ units.For a right-angled triangle,the circumradius $R$ is half of the hypotenuse.$R = \frac{c}{2} = \frac{25}{2} = 12.5$ units.Alternatively,using the general formula $R = \frac{abc}{4 	imes 	ext{Area}}$,where Area $= \frac{1}{2} 	imes 15 	imes 20 = 150$.$R = \frac{15 	imes 20 	imes 25}{4 	imes 150} = \frac{7500}{600} = 12.5$ units.

List-$I$	List-$II$
$(A)$ $rr_2 = r_1r_3$	$(I)$ $\angle A = 90^{\circ}$
$(B)$ $r_1 + r_2 = r_3 - r$	$(II)$ $b^2 = c^2 + a^2$
$(C)$ $r_1 = r + 2R$	$(III)$ $\angle C = 90^{\circ}$
	$(IV)$ $\angle B = 120^{\circ}$

If the lengths of the sides of a triangle are $15, 20, 25$ units,find the circumradius of the triangle. (in $units$)

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