LK is tangent to circle J at point K. What is the length of the radius? 6/25 85/12 121/36 157/12
2 answers:
Answer:
The answer is indeed, 85/12 ; B
Using the Pythagorean theorem, you can use FOIL to solve for the hypotenuse then subtract the radius from the entire hypotenuse to find R. Since all radii are congruent.
Simplify the rest. We also know that (6+r)^2 is the hypotenuse since angle JKL is a right angle as it is perpendicular to the center and is a tangent.
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To find the height of an equilateral triangle, draw a line from the middle of the base to the vertex (meeting point) at the top of the triangle.
An equilateral triangle is also equiangular - meaning that its angles are all 60°.
By drawing a line down the middle of the triangle (see image), we effectively create a 30-60-90 triangle on both sides - the line splits the 60° angle at the top into 30 and 30, and the height line is perpendicular to the base, making a right angle.
The sides of a 30-60-90 triangle are x, 2x, and x√3, with x being the shortest side and 2x being the hypotenuse.
We already know what 2x is - it's the side length of the triangle, or 20.
If 20 = 2x, then we can easily figure out what the length of the short side, or half the base, is.
That leaves the medium-length side - the height side drawn down the middle of the triangle. Given that 20 = 2x and the last side is x√3, what is the height?
Hope this helps!
-refrac532
An equilateral triangle is also equiangular - meaning that its angles are all 60°.
By drawing a line down the middle of the triangle (see image), we effectively create a 30-60-90 triangle on both sides - the line splits the 60° angle at the top into 30 and 30, and the height line is perpendicular to the base, making a right angle.
The sides of a 30-60-90 triangle are x, 2x, and x√3, with x being the shortest side and 2x being the hypotenuse.
We already know what 2x is - it's the side length of the triangle, or 20.
If 20 = 2x, then we can easily figure out what the length of the short side, or half the base, is.
That leaves the medium-length side - the height side drawn down the middle of the triangle. Given that 20 = 2x and the last side is x√3, what is the height?
Hope this helps!
-refrac532