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In the diagram above, line BC touches the circle at point C

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In the diagram above, line BC touches the circle at point C

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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

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BTGmoderatorDC wrote:


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
To determine the area of the circle, we need to know its radius.
Question stem, rephrased:
What is the value of r?

A radius drawn to a tangent line forms a RIGHT ANGLE.
Thus, angle OCB is a right angle, with the result that triangle OCB is a right triangle.
In right triangle OCB, OB=r, BC=35, and OC=r+AB.
Applying the Pythagorean theorem, we get:
r² + 35² = (r+AB)²
r² + 35² = r² + AB² + 2(r)(AB)
35² - AB² = 2(r)(AB)

Statement 1:
Substituting AB=25 into the blue equation above, we get:
35² - 25² = 2(r)(25)
Since we can solve for r, SUFFICIENT.

Statement 2:
Since the prompt itself indicates that angle OCB is a right angle, Statement 2 offers no new information.
INSUFFICIENT.

The correct answer is A.

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