Answer:
22.5 is the required length of PO.
Step-by-step explanation:
Explanation:
Given, length of the tangent PB = 20cm
length of the chord AB = 24cm
and the distance between the chord and centre = 5 cm
Let the distance between the chord and the centre OM and we know that a line passes through the centre of a circle ,then the line bisects that chord of the circle.
Therefore , AM = MB = 12cm
Step 1:
Now join OB .
In right angle triangle OMB
[tex]OB^{2}= OM^{2}+ MB^{2}[/tex] ...........(i) (by pythagoras theorem)
we have , OM = 5cm and MB = 12cm
Put the given value in equation (i)
∴ [tex]OB^{2} =(5)^{2} +(12)^{2}[/tex]
= 25 +144=169
[tex]OB = \sqrt{169} = 13[/tex]cm .
Step 2:
Here we see that radius OB is perpendicular of tangent PB
Now in right angle triangle OBP
we have , [tex]OP^{2}= OB^{2} +PB^{2}[/tex]
put the value of OB and PB
∴ [tex]OP^{2} = (13)^{2} +(20)^{2}[/tex] (length of tangent = 20 cm given)
= 169 +400 = 509
[tex]OP = \sqrt{509}[/tex] =22.5 cm
Final answer :
Hence , the length of PO is 22.5 cm .