Multiple choice

Two circles with centres O and O' of radii 3 cm and 4 cm, respectively intersect at two points P and Q such that OP and O'P are tangents to the two circles. Find the length of the common chord PQ.

  1. 4.8

  2. 5.4

  3. 3.2

  4. 7.9
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let O=(0,0), O'=(d,0). Radii 3, 4. Tangents at P imply triangle OPO' is right-angled at P. O'P^2 + OP^2 = OO'^2. 3^2 + 4^2 = 5^2. Distance OO' = 5. Height of triangle OPO' to hypotenuse = (3*4)/5 = 2.4. Common chord PQ = 2 * 2.4 = 4.8.

AI explanation

Since OP and O'P are tangents, the radii OP and O'P are perpendicular to each other, making triangle OPO' a right triangle with legs 3 and 4, so the hypotenuse OO' is 5. Using the formula for the common chord length, 2 times OP times O'P divided by OO', we get 2 times 3 times 4 divided by 5. This gives 24 divided by 5, which equals 4.8 cm.

Keep practicing — related questions