Q12. - Geometry

Question

To find the position of the center of circle respect to $\overrightarrow{XY}$ .

Step-by-Step Solution

Answer

The center lies in the perpendicular bisector $XY$ and is equidistant from the points $X$ and $Y$. 

Step 1. Given information.

  Line $l$; points $X$and $Y$ .

A circle through $Y$and  tangent to $l$at $X$ .

Given figure,  

Step 2. Concept Used.

 Observe the figure. 

  Draw $\overrightarrow{XY}$.

  Construct a perpendicular bisector of $\overrightarrow{XY}$as shown below.

Note that the center lies in the perpendicular bisector  $\overrightarrow{XY}$and is equidistant from the points $X$and $Y$.