Multiple choice

When chords AB and CD of a circle extended in such a way that intersect at a point P outside of the circle. If AB= 6 cm, CD= 3cm and PD= 5cm , then PB is equal to ?

  1. 6

  2. 6.25

  3. 5

  4. 4

Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For chords intersecting outside a circle: PA * PB = PC * PD. Given AB=6, CD=3, PD=5. Let PC=x. Then x(x+3) = (PB-6)(PB). Also CD=3 means x(x+3) = 3*5 = 15. So x=2.5. If PA=PB-6, then (PB-6)PB = (x+3)(x+3+x+3-3) = 5.5*2.5 = 13.75. Solving: PB² - 6PB - 13.75 = 0. PB = 4 is a valid solution.