## Solve Lesson 58 Page 90 SBT Math 10 – Kite>

Topic

In the coordinate plane Oxygengive points USA(1 ; 1) and straight line : 3x + 4y + 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.

Find the radius of the circle (OLD)

Step 1: Calculate the distance from M to

Step 2: ConsiderMNP Everyone knows the length of the altitude line from USAcalculate 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: $${(x – 1)^2} + {(y – 1)^2} = \frac{{16}}{3}$$