Question : Let C be a circle with centre O and radius 5 cm. Let PQ be a tangent to the circle and A be the point of tangency. Let B be a point on PQ such that the length of AB is 12 cm. If the line joining O and B intersects the circle at R, find the length of BR (in cm).
Option 1: 2
Option 2: 13
Option 3: 6
Option 4: 8
Correct Answer: 8
Solution :
Given: Radius = 5 cm
OA = 12 cm
We know that the angle between a tangent to a circle and the radius through the point of contact is always a right angle.
From figure,
OA = OR = 5 cm (radius)
By applying Pythagoras theorem, we get:
$OB = \sqrt{AB^2+OA^2}$
$= \sqrt{12^2+5^2}$
$= \sqrt{144+25}$
$= \sqrt{169}=13$
OB = 13 cm
Now, OB = OR + RB
⇒ 13 = 5 + RB
Thus, RB = 8 cm
Hence, the correct answer is 8.
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