A tangent is drawn to a circle from an external point p. What is the length of the tangent? (1) The radius of the circle is given (2) The distance between the center and the point p is given.
Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
Let r be the radius and d be the distance from the center to point P. The tangent, radius, and the line from center to P form a right triangle. The length of the tangent is sqrt(d^2 - r^2). Both r and d are needed to calculate this.
The length of a tangent drawn from an external point is found using the Pythagorean theorem by subtracting the square of the radius from the square of the distance to the center. Statement 1 alone fails because it provides the radius but lacks the distance to the external point. Statement 2 alone fails because it provides the distance but lacks the radius. Combining both statements provides the two necessary variables to calculate the full length of the tangent.