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A circle k(O) with the radius r is given. Line AB is a Tangent to circle k(O) at point B. Find AB, if m∠AOB=60°, and r=12 cm.

Respuesta :

Answer:

AB = 12√3

Step-by-step explanation:

OAB is a right triangle because the OB is perpendicular to AB. Since AOB is 60°, OAB is 30°, giving us a 30-60-90 triangle. Therefore AB = OB*√3=12√3

To solve such problems we must know about the Tangent and right-angle triangle.

Part 1

Tangent

Tangent is a straight line that touches the circle at any point in its circumference. Also, a tangent is always perpendicular to the circle radius of the circle.

The value of AB is 12√3.

Part 2

Given to us,

  • Line AB is a Tangent to circle k(O) at point B,
  • Radius of circle k(O), r = 12 cm,
  • ∠AOB=60°,

Solution

A tangent is always perpendicular to the circle radius of the circle.

Also, for any right-angled triangle,

[tex]\bold{tan \theta =\dfrac{Perpendicular}{base}}[/tex]

where,

θ is the angle,

Perpendicular is the side opposite to the angle,

base is the small adjacent side of the angle,

In ΔAOB,

As we can see in the image below,

In ΔAOB, for ∠AOB,

[tex]\bold{tan(\angle{AOB})=\dfrac{Perpendicular(AB)}{Base(OB)}}}[/tex]

[tex]tan (60^o) = \dfrac{AB}{12}\\\sqrt3 = \dfrac{AB}{12}\\12\sqrt3 = AB[/tex]

Hence, the value of AB is 12√3.

Learn more about Tangent:

https://brainly.com/question/13005496

Ver imagen ap8997154

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