In a right triangle ABC the in circle touches the hypotenuse AC at O. If AD=10 and DC = 3, the inradius of ABC is

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Solution

The correct option is D 2
$(r + 3)^{2} + (r + 10)^{2} = (13)^{2}$
$\Rightarrow r^{2} + 9 + 6 r + r^{2} + 100 + 20 r = 169$
$\Rightarrow 2 r^{2} + 26 r - 60 = 0$
$\Rightarrow r^{2} + 13 r - 30 = 0$
$\Rightarrow (r + 15) (r - 2) = 0$
$r = 2$

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In a right triangle ABC the in circle touches the hypotenuse AC at O. If AD=10 and DC = 3, the inradius of ABC is

The correct option is D 2(r+3)2+(r+10)2=(13)2⇒r2+9+6r+r2+100+20r=169⇒2r2+26r−60=0⇒r2+13r−30=0⇒(r+15)(r−2)=0r=2

The correct option is D 2
$(r + 3)^{2} + (r + 10)^{2} = (13)^{2}$
$\Rightarrow r^{2} + 9 + 6 r + r^{2} + 100 + 20 r = 169$
$\Rightarrow 2 r^{2} + 26 r - 60 = 0$
$\Rightarrow r^{2} + 13 r - 30 = 0$
$\Rightarrow (r + 15) (r - 2) = 0$
$r = 2$