Determine whether a tangent line to circle O is shown in the diagram, for AB = 7, OB = 3.75, and AO = 8. Explain your reasoning. (The figure is not drawn to scale.)

Question

contestada

Respuesta :

calculista calculista · Answer 1 · 2020-04-15T13:41:35+02:00

Answer:

The line AB is not tangent to circle O

Step-by-step explanation:

we know that

If AB is tangent to circle O at point B

then

AB is perpendicular to OB (radius) and ABO is a right triangle

Verify

Applying the Pythagorean Theorem

[tex]AO^2=AB^2+OB^2[/tex]

substitute the given values

[tex]8^2=7^2+3.75^2[/tex]

[tex]64=49+14.0625[/tex]

[tex]64=63.0625[/tex] -----> is not true

so

The triangle not satisfy the Pythagorean Theorem

therefore

The line AB is not tangent to circle O