In Delta ABC,m angle B = 90^{circ}. A circle | vedclass

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(B) In a right-angled triangle,the radius $r$ of the incircle is given by the formula $r = \frac{AB + BC - AC}{2}$.First,calculate the hypotenuse $AC$

Vedclass · Accepted Answer

$6$

Vedclass · Answer

(B) In a right-angled triangle,the radius $r$ of the incircle is given by the formula $r = \frac{AB + BC - AC}{2}$.First,calculate the hypotenuse $AC$ using the Pythagorean theorem: $AC = \sqrt{AB^2 + BC^2} = \sqrt{16^2 + 30^2} = \sqrt{256 + 900} = \sqrt{1156} = 34$.Now,substitute the values into the formula: $r = \frac{16 + 30 - 34}{2}$.$r = \frac{46 - 34}{2} = \frac{12}{2} = 6$.Thus,the radius of the circle is $6$.

In $\Delta ABC$,$m \angle B = 90^{\circ}$. $A$ circle is inscribed in $\Delta ABC$ touching all its sides. If $AB = 16$ and $BC = 30$,find the radius of the circle.

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