Question

How do I answer this question-

Answer 1

9514 1404 393

Answer:

  18 cm

Step-by-step explanation:

Consider right triangle PCA.

The length PC is the hypotenuse of that triangle. It is also the radius of the circle: 15 cm.

The length AC is AB -CB = (27 -15) cm = 12 cm.

The length AP can be found from the Pythagorean theorem:

  AP² +AC² = PC²

  AP² = PC² -AC² = (15 cm)² -(12 cm)² = (225 -144) cm² = 81 cm²

  AP = √(81 cm²) = 9 cm

Since A is the midpoint of PQ, the length of PQ is double the length of AP:

  PQ = 2·AP = 2·9 cm

  PQ = 18 cm