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**Hint:**From the figure AB is the diameter and the angle so inscribed in the semicircle by that diameter is a right angle. So \[\angle APB = {90^ \circ }\]. Thus we can use Pythagoras theorem to find the side PB by taking diameter as the hypotenuse. Let’s solve it.

**Step by step solution:**

Given that AB is a diameter of the circle and the angle formed by the diameter is a right angle.

So using the Pythagoras theorem,

\[A{B^2} = A{P^2} + P{B^2}\]

To find PB,

\[ \Rightarrow P{B^2} = A{B^2} - A{P^2}\]

Putting the values,

\[ \Rightarrow P{B^2} = {13^2} - {12^2}\]

\[ \Rightarrow P{B^2} = 169 - 144\]

\[ \Rightarrow P{B^2} = 25\]

Taking the square root on both sides,

\[ \Rightarrow PB = 5cm\]

**This is the length of side PB of the triangle so formed \[ \Rightarrow PB = 5cm\]**

**Note:**

Students don’t consider that AP and PB are both chords so they will measure the same length. Also it is not given that both the base angles are of \[{45^ \circ }\]. So we have enlisted the property that the angle formed by the diameter is a right angle. So go with it only.

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