Let A B C D be a quadrilateral with area 18 , with side A B parallel to the side C D and A B=2 C D. Let A D be perpendicular to A B and C D. If a circle is drawn inside the quadrilateral A B C D touching all the sides, then its radius is

Question

Let A B C D be a quadrilateral with area 18 , with side A B parallel to the side C D and A B=2 C D. Let A D be perpendicular to A B and C D. If a circle is drawn inside the quadrilateral A B C D touching all the sides, then its radius is (A) 3 (B) 2 (C) 3 / 2 (D) 1

Tardigrade Admin · Accepted Answer

18=(1/2)(3 α)(2 r) α r=6 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/35ea43bfeb027147438c09536a253936-.png" /> Line, y=-(2 r/α)(x-2 α) is tangent to circle (x-r)2+(y-r)2=r2 2 α=3 r and α r=6 r=2

Q. Let $A BC D$ be a quadrilateral with area 18 , with side $A B$ parallel to the side $C D$ and $A B = 2 C D$ . Let $A D$ be perpendicular to $A B$ and $C D$ . If a circle is drawn inside the quadrilateral $A BC D$ touching all the sides, then its radius is

3

2

$3/2$

1

$18 = \frac{1}{2} (3 α) (2 r) α r = 6$

Line, $y = - \frac{2 r}{α} (x - 2 α)$ is tangent to circle
$(x - r)^{2} + (y - r)^{2} = r^{2}$
$2 α = 3 r$ and $α r = 6$
$r = 2$

Q. Let ABCD be a quadrilateral with area 18 , with side AB parallel to the side CD and AB=2CD. Let AD be perpendicular to AB and CD. If a circle is drawn inside the quadrilateral ABCD touching all the sides, then its radius is

3

2

3/2

1

18=21​(3α)(2r)αr=6 Line, y=−α2r​(x−2α) is tangent to circle (x−r)2+(y−r)2=r2 2α=3r and αr=6 r=2

Q. Let $A BC D$ be a quadrilateral with area 18 , with side $A B$ parallel to the side $C D$ and $A B = 2 C D$ . Let $A D$ be perpendicular to $A B$ and $C D$ . If a circle is drawn inside the quadrilateral $A BC D$ touching all the sides, then its radius is

$3/2$

$18 = \frac{1}{2} (3 α) (2 r) α r = 6$

Line, $y = - \frac{2 r}{α} (x - 2 α)$ is tangent to circle
$(x - r)^{2} + (y - r)^{2} = r^{2}$
$2 α = 3 r$ and $α r = 6$
$r = 2$