Multiple choice

Two chords AB and CD of a circle when produced, meet at a point P outside the circle. If AB = 6 cm, PB = 5 cm, PD = 4 cm, then CD is equal to

  1. 8.25 cm

  2. 7.5 cm

  3. 9.75 cm

  4. 7.75 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

By the secant-secant theorem, PA * PB = PC * PD. Here, PA = AB + PB = 6 + 5 = 11. So, 11 * 5 = PC * 4, which means PC = 55 / 4 = 13.75. Since PC = PD + CD, 13.75 = 4 + CD, so CD = 9.75 cm.

AI explanation

By the property of intersecting secants outside a circle, PA multiplied by PB equals PC multiplied by PD. Substituting the values gives PA multiplied by 5 equals PC multiplied by 4, and since PA equals AB plus PB at 11 cm, we have 55 equals 4 multiplied by PC. Solving gives PC as 13.75 cm, and since CD equals PC minus PD, CD equals 13.75 minus 4 which is 9.75 cm.

Keep practicing — related questions