`A B` is a diameter of a circle. `P` is a point on the semi-circle `A P BdotA Ha n dB K` are perpendiculars from `A and B` respectively to the tangent at `P`. Prove that `A H+B K=A B`.

Explanation

` angle MPO=90^{circ}`


As `BK bot HM, AH bot HM and OP bot HM`


So, `AH|OP| BK`


Assume `AH=x, BK=y and OP=r BM=z`.


In `triangle MKB and triangle MHA`


`angle MKB=angle MHA=90^{circ}`


` angle BMK=angle AMH`


By AA criterion of similarity,


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