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is tangent to circle G at point F.

Circle G is shown. Line segment G F is a radius. Line segment F H is a tangent that intersects the circle at point F. A line is drawn from point H to point G and goes through a point on the circle. The length of F H is 35, and the length of the line segment from point H to the point on the circle is 25. The lengths of the radii are r.

What is the length of the radius, r?

10 units
12 units
20 units
24 units

Respuesta :

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Answer:

12

Step-by-step explanation:

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The length of the radius r is given as 12 units

The figure described forms a right angle triangle solved using Pythagoras theorem.

What is the Pythagorean theorem?

The theorem says that the square of the hypotenuse is equal to the square of the opposite side plus square of the adjacent.

c² = a² + b²

The hypotenuse = radius +25

Opposite = radius

Adjacent = 35

Let the radius be r

(r + 25)² = r² + 35²

(r + 25)(r + 25) = r² + 35²

r² + 50r + 625 = r² + 1225

50r = 1225 - 625

r = 600/50

r = 12

The length of the radius is given as 12 units.

Read more on Pythagorean theorem here https://brainly.com/question/343682