Hard
Two concentric circles have radii 5 cm and 3 cm. A chord of the larger circle touches the smaller circle. Find the length of the chord.
Explanation
Explanation
Step 1: Let O be the common centre. The chord AB of the big circle touches the small circle at P. So AB is a tangent to the small circle at P.
Step 2: The radius to the point of contact is perpendicular to the tangent, so OP ⊥ AB, with OP = 3 cm.
Step 3: In right triangle OPA: OA = 5 cm (radius of big circle), OP = 3 cm. By Pythagoras, AP² = 5² − 3² = 25 − 9 = 16, so AP = 4 cm.
Step 4: The perpendicular from the centre bisects a chord, so P is the midpoint of AB and AB = 2 × AP = 8 cm.
Answer: 8 cm.
PRO TIP
Re-check your working by substituting the answer back into the original question.