So I have a problem that reads as follows:
[PQ] is a chord of a circle. R lies on the major arc of the circle. Tangents are drawn through P and through Q. From R, perpendiculars [PA], [PB] and [PC] are drawn to the tangent at A, the tangent at B and [AB] respectively. Prove that RA.RB = RC^2.
It's not that I don't get similarity, it's rather the phrasing of the problem...how can you have perpendiculars PA, PB and PC from R???
A simple drawing would explain it.the phrasing is the problem
Unfortunately, I do not understand the phrasing well enough to construct a sketch.
You are drawing tangents to A and B, therefore A & B must be on the circle. It does not so state but C can be anywhere.
If D is on the line PA, then line RD is perpendicular to line PA; it is a line perpendicular to PA that passes through point R.how can you have perpendiculars PA from R???