Option C:
[tex]b=3\sqrt{13}[/tex]
Solution:
Given PM = 4 and MY = 9
Let us first find the value of c:
By the geometric mean of similar right triangles,
[tex]DM^2=PM\times MY[/tex]
[tex]c^2= 4\times 9[/tex]
[tex]c^2= 36[/tex]
Taking square root on both side of the equation, we get
c = 36
[tex]DY^2=MY(PM + MY)[/tex]
[tex]b^2=9(4+9)[/tex]
[tex]b^2=9\times 13[/tex]
[tex]b^2=117[/tex]
Taking square root on both side of the equation, we get
[tex]b=3\sqrt{13}[/tex]
Option C is the correct answer.
Hence the value of b is [tex]3\sqrt{13}[/tex].
