1. ## Similarity problem, tangents

Hi,
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???

2. Originally Posted by HelenaStage
Hi,
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 from R???

You can't !

At least not until you define where points A, B and C are.
The problem is incomplete in its current form.

3. Originally Posted by bowline
You can't !

At least not until you define where points A, B and C are.
The problem is incomplete in its current form.
That's all the info I get...

4. Originally Posted by HelenaStage
Hi,
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 from R???
the phrasing is the problem
A simple drawing would explain it.
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.

how can you have perpendiculars PA from R???
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.

5. Originally Posted by aidan
A simple drawing would explain it.
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.
Yes, OK, but the problem says perpendiculars PA, PB and PC...?

I believe point C will be the result of a line from R cutting the line joining A and B...

6. Originally Posted by HelenaStage
[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.
That's all the info I get...
See the attached sketches for my initial understanding of the question.

7. Since I'm limited to attaching 5 files
this is a continuation of the above: