Answer:
not a tangent
Explanation:
You want to know if a segment 19 units long from a point 25 units from the center of a circle of radius 14 units is a tangent.
Pythagorean theorem
A tangent to a circle forms a right angle with the radius to the point of tangency. You can easily check to see if the triangle shown is a right triangle by using the Pythagorean theorem.
If the triangle is a right triangle the sum of the squares of the short sides is equal to the square of the hypotenuse:
14² +19² = 25²
196 +361 = 625
557 = 625 . . . . . . . . false — not a right triangle; not a tangent
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Additional comment
The attached figure is drawn to scale. It shows line QR intersects the circle in 2 places, so is not a tangent. The angle at Q is obtuse.
Given 3 sides of a triangle, you can classify it as acute, right, or obtuse using the "form factor" computed as follows. Form the sum of the squares of the two shorter sides, and subtract the square of the longer side:
f = 14² +19² -25² = 196 +361 -625 = -68
The interpretation is ...
- f < 0 — obtuse triangle
- f = 0 — right triangle
- f > 0 — acute triangle