Im not sure how to answer this.

PS AND PT are two tangents draw from a point P to a circle whose centre is O. Join PO and prove that PT = PS.

I drew the diagram out and so I would end up with two right angled triangles meaning I'd have 90 degrees and r = SO = TO, but from there I am not quite sure how to prove it.

Thank you!


You have a common side (hypotenuse) PO in both the right angled triangles POS and POT. The side OS=OT as you mentioned. So PT=PS by Pythagoras. In fact, triangles POT and POS are congruent

  • $\begingroup$ So if i were to write an answer down I would say that SO^2 + PS^2 = PO^2 and TO^2 + PT^2 = PO ^2 therefore PT = PS? $\endgroup$ – user639649 Apr 4 at 1:38
  • $\begingroup$ Yes, a better way would be: $PT^2=PO^2-OT^2=PO^2-OS^2=PS^2$. Therefore, $PT=PS$ $\endgroup$ – Tojrah Apr 4 at 1:47

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