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kotegsom [21]
3 years ago
5

Select whether to use the Pythagorean Theorem or its converse in each situation.

Mathematics
1 answer:
alina1380 [7]3 years ago
3 0
The side is 15ft long
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uranmaximum [27]

Answer:

r=  \frac{ |c - lg  -  fm| }{ \sqrt{ {l}^{2} +  {m}^{2}  } }

Step-by-step explanation:

The given circle has equation

{x}^{2}  +  {y}^{2}  + 2gx + 2fy + c = 0

This circle has centre (-g,-f).

For the line

lx + my + n = 0

to be a tangent to this circle, the perpendicular distance from the center to this line must be equal to the radius of the circle.

This is given by:

d =  \frac{ |ax + by + c| }{ \sqrt{ {a}^{2} +  {b}^{2}  } }

We substitute the center and radius to get:

r=\frac{ |l \times  - g + m \times  - f+ c| }{ \sqrt{ {l}^{2} +  {m}^{2}  } }

We simplify to get;

r=  \frac{ |c - lg  -  fm| }{ \sqrt{ {l}^{2} +  {m}^{2}  } }

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