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Line segment KL is tangent to circle J at point K.



What is the length of the radius, r?

A) 8 units
B) 10 units
C) 12 units
D) 16 unit

Line segment KL is tangent to circle J at point K What is the length of the radius r A 8 units B 10 units C 12 units D 16 unit class=

Respuesta :

calculista

we know that

if the line segment KL is tangent to circle J at point K

then

KL is perpendicular to KJ

the triangle KJL is a right triangle

Applying the Pythagorean Theorem

[tex]LJ^{2} =KL^{2}+KJ^{2}[/tex]

we have

[tex]KL=24\ units\\KJ=r\ units\\JL=(16+r)\ units[/tex]

substitute the values

[tex](16+r)^{2} =24^{2}+r^{2}\\256+32r+ r^{2}=576+ r^{2} \\32r=576-256 \\r= 320/32\\r=10\ units[/tex]

therefore

the answer is the option B

[tex]10\ units[/tex]

The length of the radius r of the given triangle is; B: 10 units

Pythagoras Theorem

We can see a circle and a triangle from the image given. Now, the one that we are most concerned with is the Triangle since that is what we can use to determine the radius of the circle of which it is a tangent.

Now, we see that triangle JKL is a right angle triangle.

Thus using Pythagoras theorem;

r² + 24² = (r + 16)²

r² + 576 = r² + 32r + 256

r² will cancel out to give;

576 - 256 = 32r

320 = 32r

r = 320/32

r = 10 units

Read more about Pythagoras theorem at; https://brainly.com/question/1783328

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