Question

Which of the following statements is/are correct?

1. The locus of the point of intersection of two perpendicular tangents is called director circle of the given circle.

2. The director circle of a circle is concentric circle.

3. The radius of director circle of a circle is equal to the radius of original circle.C

• A. Only 1 & 2
• B. Only 1
• C. Only 1 & 3
• D. All 1, 2 and 3

Answer 1

The correct option is A

Only 1 & 2

Definition of director circle of a circle:It is the locus of the point of intersection of two perpendicular tangents.

Director circle of a circle is also concentric to original circle.

In the given figure we have drawn the locus of perpendicular tangents (OR) director circle.

$\angle PAQ={90}^{\circ }$

Line AC divides angle APQ in two equal parts.

$\angle PAC={45}^{\circ }$

In $\Delta PAC$

$\sin {45}^{\circ }=\frac{r}{AC}$

$AC=\frac{r}{\sin {45}^{\circ }}=\frac{r}{\frac{1}{\sqrt{2}}}=\sqrt{2}r$

$AC=\sqrt{2}r$

Radius of director circle of a circle =$\sqrt{2}$ time of radius of original circle.

statement 3 is wrong.

So, only statement 1 & 2 are constant.