If AO = 30, BC = 48 then, AB = 72.
What is tangent?
"Tangent to a circle is the line that touches the circle at only one point."
"A tangent to a circle is always perpendicular to the radius of a circle."
For given question,
AB is tangent to circle.
Also, AO = 30, BC = 48
From figure, we can observe that,
AO = CO .......................(radius of circle)
⇒OC = 48
Also,
OB = OC + BC
⇒ OB = 30 + 48
⇒ OB = 78
We know, a tangent to a circle is always perpendicular to the radius of a circle.
⇒ AB ⊥ AO
This means, ΔAOB is right triangle.
Using Pythagoras theorem to right triangle AOB,
⇒ [tex](OB)^{2} = (AO)^{2} + (AB)^{2}[/tex]
⇒ [tex](AB)^2 = (OB)^{2} - (AO)^{2}[/tex]
⇒ [tex](AB)^2=(78)^2-(30)^2[/tex]
⇒ [tex](AB)^2=5184[/tex]
⇒ [tex]AB=\sqrt{5184}[/tex]
⇒ [tex]\bold{AB=72}[/tex]
Therefore, option (D) is the correct answer.
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