For this case, we know that:
[tex] PA = PB [/tex]
Then, by Pythagorean theorem (right triangle on the right) we have:
[tex] CP ^ 2 = CB ^ 2-PB ^ 2 [/tex]
So, again using the Pythagorean theorem (right triangle on the left) we have:
[tex] CA ^ 2 = CP ^ 2 + PB ^ 2 [/tex]
Substituting values:
[tex] CA ^ 2 = (CB ^ 2-PB ^ 2) + PB ^ 2 [/tex]
Rewriting:
[tex] CA ^ 2 = CB ^ 2 [/tex]
[tex] CA = CB [/tex]
[tex] CA = 15 [/tex]
Answer:
The value of CA is given by:
[tex] CA = 15 [/tex]
