Question

A circle touches all side of a parallelogram so that parallelogram must be-

• A. rectangle
• B. rhombus
• C. square
• D. trapezium

Answer 1

The correct option is B rhombus

A circle touches all side of a parallelogram must be a rhombus.

So, option B is correct.

Given - $AB=CD$

$BC=AD$

Now, $AP=AS$

If from one external point, two tangents are drawn two circle then have equal tangent segments.

So, $AP=AS$ [tangent from point A] ------(1)

$\Rightarrow BP=BQ$ [tangent from point B] ---------(2)

$\Rightarrow CR=CQ$ [tangent from point C] ---------(3)

$\Rightarrow DR=DS$ [tangent from point D] ----------(4)

equation $\left(1\right)+\left(2\right)+\left(3\right)+\left(4\right)$

$AP+BP+CR+DR=AS+BQ+CQ+DS$

$AB+DC=AD+BC$ [from diagram]

$2AB=2AD$ from $⊛$

$AB=AD$ And from $⊛$ AB=CD and BC=AD

So, $AB=BC=CD=AD$

It is rhombus.