To solve this problem, we can use the Pythagorean theorem.
Given:
OP = 12 cm (length of the radius)
O is the center of the circle with a radius of 5 cm.
Let's denote PQ as x.
According to the Pythagorean theorem, in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, OQ is the hypotenuse, and the sides of the triangle are OP and PQ.
Applying the Pythagorean theorem:
OQ² = OP² + PQ²
Substituting the given values:
(5 cm)² = (12 cm)² + PQ²
25 cm² = 144 cm² + PQ²
PQ² = 25 cm² - 144 cm²
PQ² = -119 cm²
Since the result is negative, it indicates that there is no real solution for PQ. Therefore, none of the provided options (a), (b), (c), or (d) is the correct answer.
