Q4 of 23 Page 1

Solve any two sub-questions:

Prove that “The length of the two tangent segments to a circle drawn from an external point are equal.”

The figure is as follows:


Given:


A circle with centre O, an external point P of the circle. The two tangents through the point P touches the circle at the points A and B.


To prove that PA = PB


Construction:


Draw the segment OA, segment OB and segment OP.


Proof:


∠ PAO = ∠ PBO ... (Radius is perpendicular to tangent)


In the right angled ∆ PAO and the right angled ∆PBO.


Segment OA ≅ segment OB ... (Radii of same circle)


Hypotenuse PO ≅ hypotenuse PO ... (common side)


∆ PAO ≅ ∆ PBO ... (Hypotenuse side theorem)


∴ Segment PA ≅ segment PB ... (c.s.c.t)


∴ PA = PB


Hence Proved.


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