Answer:
The length of OA = 10 cm
Explanation:
* Lets revise some facts about the circle
- If two tangents drawn from a point outside the circle, then
they are equal in lengths
- The radii of the circle are perpendicular to the tangents at the
point of tang-ency
- The line from the center to the angle between the two tangents
bisects it
* Now lets solve the problem
∵ The sides of ∠A are tangents to circle O
∴ The radius of the circle O ⊥ to the tangent at the point of tang-ency
∴ The line OA bisects ∠A
- The measure of ∠A = 60°
∴ The measure of the angle between line OA and the tangent
is equal to 1/2 × 60° = 30°
* Now we have right angle triangle formed from the line OA as a
hypotenuse two legs of the right angle one of them is the
tangent and the other is the radius
∵ r = 5 cm
∵ The measure of the angel opposite to r is 30°
∵ OA is the hypotenuse
- By using trigonometry function
∴ sin(30°) = 5/OA
∵ sin(30°) = 1/2
∴1/2 = 5/OA ⇒ by using cross multiplication
∴ OA = 2 × 5 = 10 cm
* The length of OA = 10 cm