Loci circle question

29 Views Asked by At

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!

1

There are 1 best solutions below

2
On BEST ANSWER

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