Question

plz help mi with this prbl.

Answer 1

Given AP = 24cm and PB = 6cm.

Then diameter AB = AP + PB

                                = 24 + 6

                                = 30cm.


Now,

We have to draw perpendicular point on point P. Hence the smallest chord that passes through Point P is CD.

Then radius AO = OB = 15cm.

We know that

OC = 15cm = Radius

OP = AP - AO

      = 24 - 15

      = 9


By the Pythagorean theorem, we get

OC^2 = OP^2 + CP^2

15^2 = 9^2 + CP^2

CP^2 = 225 - 81

CP^2 = 144

CP^2 = 12

So, CD = 24cm.



Therefore the length of the shortest chord = 24cm.


Hope this helps!