find the lengrh of PQ

Question

the two circles with centres A and B; radii 5 cm and 3 cm respectively, touching each other internally. if the perpendicular bisector of AB meets the bigger circle in P and Q

Answer 1

The length of AB is 2 cm, so A and the midpoint of AB are 1 cm apart, and this half of AB forms a right triangle with P.  Since P is on the bigger circle, the length of AP is 5 cm is the length of the hypotenuse.  By the Pythagorean Theorem, a² + (1 cm)² = (5 cm)².  Solve for a, and you get half the length of PQ.