Can this question be answered using similar triangles?

I considered triangles POA and PBC as similar triangles and still got the right answer.

<OPA is common for both the triangles and the tangents to the circles give right angles.

It’s not POA and PBC though - it’s PAO and PBC, right? The ordering of the triangle vertices is very important.

Could you please explain further?

So if you say that POA and PBC are similar, you’re telling that

angles P and P are equal (correct)

angles O and B are equal (incorrect - because only C is right-angled)

angles A and C are equal (again wrong - only angle A is right-angled)

I think I got it now. I considered angle B and angle A to be 90 and hence equal. Didn’t consider the vertices.