CircleHard

Question

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

Options

A.3
B.2
C.3/2
D.1

Solution

           
18 = (3α)(2r)     ⇒ αr = 6
Line y = - (x - 2α) is tangent to (x - r)2 + (y - r)2 = r2
2α = 3r and αr = 6
r = 2.

Create a free account to view solution

View Solution Free
Topic: Circle·Practice all Circle questions

More Circle Questions

Tangents OP and OQ are drawn from the origin O to the circle x2 + y2 + 2gx + 2fy + c = 0. Then, the equation of the circ...Equations of circles which pass through the points (1, _2) and (3, _ 4) and touch the x-axis is...Let $\overrightarrow{c}$ and $\overrightarrow{d}$ be vectors such that $|\overrightarrow{c} + \overrightarrow{d}| = \sqr...If (4, 3) and (−12, −1) are end points of a diameter of a circle, then the equation of the circle is-...If 2f(tx)dt = f(x) +1, where f(x) is non constant function, then y = f(x) represents -...