Q. 4 A5.0( 3 Votes )

Solve any two sub

Answer :

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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