a tangent drawn from a point p lying in the exterior of the circle has more length than the radius
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data;a circle with o and a tangent xy to the circle at a point p
to prove;op is perpendicular to xy
construction;draw a point q on yx other than p and join oq
proof;the point q must lie out side the circle
*oq is longer than the op of the circle is oq greater than op
*since for every point on the line xy except the point p.op is the shortest of all the distance of the o point xy. so op is perpendicular to xy
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true
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