Question

converse of tangent theorem


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Answer 1

Answer:

Let D be a point outside a circle ABC.

Let DA be a straight line which cuts the circle ABC at A and C.

Let DB intersect the circle at B such that DB2=AD⋅DC.

Then DB is tangent to the circle ABC.

In the words of Euclid:

If a point be taken outside a circle and from the point there fall on the circle two straight lines, if one of them cut the circle, and the other fall on it, and if further the rectangle contained by the whole of the straight line which cuts the circle and the straight line intercepted on it outside between the point and the convex circumference be equal to the square on the straight line which falls on the circle, the straight line which falls on it will touch the circle.

Answer 2

Answer:

Tangent to a Circle Theorem: a line is tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency. ... Therefore, the converse of this theorem is also true.