Constructing tangents from circle...?

Question

How do you construct a tangent to the circle at point P?

(I have a link below)

Answer 1

Here are the steps:
1. Connect the center of the circle and P
2. Construct the perpendicular bisector of the line you just drew so it passes through the center of the circle
3. Connect point P with the point where the perpendicular bisector intersects the circumference of the circle
That is your line of tangency. Don't forget to extend it!

Answer 2

Is this one of those problems which have to be solved with the ruler andthe compass only?

If so, here it is. First, the analysis:
Assume you have the tangent point T. Then OT is perpendicular on PT, so the triangle OTP has a right angle at T. A right triangle has the nice property that its hypothenuse (OP in this case) is the diameter of the circumscribed circle, therefore its center is halfway between O and P.Therefore,
1. Connect O and P, and find the middle of the segment, call it Q.
2. Draw a circle with the center in Q and passing through O and P. This circle will intersect your circle in two points, which according to the reasoning above, are the points through which the tangents from P to the circle will pass.

Answer 3

The first thing you need to do is actually *find* the centre.
To do this, join P to any two different points on the circle, Construct the perpendicular bisectors of those two lines and the intersection is the centre O.

Next, draw OP. Extend it so that it is more than twice the length of OP.

With compass centerd at P, open to O and swing around so you cut OP again at Q. P is in the middle of O and Q [in the diagram as well as the alphabet].

Construct the perpendicular bisector of OQ.

Answer 4

Call the center of the circle O.
Draw the line PO
Draw the perpendicular bisector of PO bisecting PO at M.
Now put the compass point at M and stretch it out to O.
Now Draw an arc that passes through circle at two points A and B. Now draw a line from P to A and from P to B.

PA and PB are the two possible tangents from the point P.

Answer 5

Draw a radius from the center going directly upward to a point on the circle and do the same going the opposite way, again from the center of the circle.

The two points on the circle drawn from the circle are tangent to the circle at two locations.

Then draw two lines going from the first point tangent to the circle to the outside point P and then another line from the second point tangent to the circle going to the same outside point P.

Guido

Answer 6

Place the ruler on top of the two circles then draw your line