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**Topic**

In the coordinate plane *Oxygen*give points *USA*(1 ; 1) and straight line : 3*x* + 4*y* + 3 = 0. Write the equation of the circle (*OLD*), know (*OLD*) has a mind *USA* and straight line* *cut (*OLD*) at two points *WOMEN*, *P* satisfy the triangle *MNP* even.

**Solution method – See details**

Find the radius of the circle (*OLD*)

Step 1: Calculate the distance from M to

Step 2: Consider*MNP* Everyone knows the length of the altitude line from *USA*calculate the lengths of the sides of the triangle as the radius of (*OLD*)

Step 3: Write a circle PT with center *USA* and the radius found in step 2

**Detailed explanation**

Call *H* is the projection of *USA* go straight

We have: \(MH = d(M,\Delta ) = \frac{{\left| {3 + 4 + 3} \right|}}{{\sqrt {{3^2} + {4^2} } }} = 2\)

According to the assumption,*MNP* evenly \( \Rightarrow \widehat {MNH} = {60^0}\)

Consider \(\Delta MNH\) square at *H* yes \(MN = \frac{{MH}}}{{\sin \widehat {MNH}}} = \frac{2}{{\sin {{60}^0}}} = \frac{{4\sqrt 3 }}{3}\)\( \Rightarrow R = \frac{{4\sqrt 3 }}{3}\)

So (*OLD*) has PT: \({(x – 1)^2} + {(y – 1)^2} = \frac{{16}}{3}\)

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