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

[BTGmoderatorDC]

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

[Jay@ManhattanReview]

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
_________________
Manhattan Review

Locations: Manhattan Review Visakhapatnam | GMAT Prep Warangal | GRE Prep Dilsukhnagar | Begumpet GRE Coaching | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.