BTGmoderatorDC wrote: ↑Thu Jan 16, 2020 6:22 pm
In the diagram above, line BC touches the circle at point C, and the distance from B to C is 35 cm. What is the area of the circle?
(1) AB = 25 cm
(2) Angle OCB = 90°
OA
A
Source: Magoosh
Since BC is a tangent, the angle OCB = 90º; thus, ∆OCB is a rightangled triangle. So, OB is the hypotenuse and BC and OC are two legs.
Say OC = OA = r
Thus, OB = OA + AB = r + AB
Applying Pythagoras theorem, we have
OB^2 = OC^2 + BC^2
(r + AB)^2 = r^2 + 35^2
If we get the value of AB, we get the value of r, thus, the area of the circle. Statement 1 provides the value of AB. So, Statement 1 itself is sufficient.
The correct answer:
A
Hope this helps!
-Jay
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