Two circles with centres O and Q and radii 8cm intersect at points A and B. The distance between O and Q is 12cm. The line AB meets OQ at X. a) the length of the chord AB.

Question 18:
Two circles with centres O and Q and radii 8cm intersect at points A and B. The distance between O and Q is 12cm. The line AB meets OQ at X.

a) the length of the chord AB.

Step 1: Draw a diagram and identify the given lengths.
Let $r$ be the radius of each circle, so $OA = OB = QA = QB = 8 \text{ cm}$.
The distance between the centers is $OQ = 12 \text{ cm}$.
The line segment AB is the common chord. The line connecting the centers OQ is the perpendicular bisector of the common chord AB. This means $