Answer: The correct question is "Segments AB and BC are both tangent to the circle shown above. What is the value of x"
The value of x is also 5 units , by tangent rule.
Explanation:
The Two Tangent Theorem:
The two tangent theorem states that if we draw two lines from the same point which lies outside a circle, such that both lines are tangent to the circle, then their lengths are the same.
We will now prove that theorem.
Problem
AB and AC are tangent to circle O. Show that AB=AC
Proof of the Two Tangent Theorem
(1) AB is tangent to Circle O //Given
(2) ∠ABO=90° //tangent line is perpendicular to circle
(3) AC is tangent to Circle O //Given
(4) ∠ACO=90° //tangent line is perpendicular to circle
(5) AO=AO //common side (reflexive property)
(6) OC=OB=r //radii of a circle are all equal
(7) △ABO≅△ACO //Hypotenuse-leg
(8) AB=AC // Corresponding sides in congruent triangles (CPCTC)
Therefore, segment AB = BC = 5 units