Tangent to a circle: A line which intersects a circle at any one point is called the tangent.
Construction: Draw a circle with centre O. Draw a tangent XY which touches point P at the circle.
To Prove: OP is perpendicular to XY.
Draw a point Q on XY; other than O and join OQ. Here OQ is longer than the radius OP.
OQ > OP
For every point on the line XY other than O, like Q1, Q2, Q3, ....Qn;
OQ1 > OP
OQ2 > OP
OQ3 > OP
OQn > OP
Since OP is the shortest line
Hence, OP ⊥ XY proved
Construction: Draw a circle with centre O. From a point P outside the circle, draw two tangents P and R.
To Prove: PQ = PR
In Î” POQ and Î” POR
OQ = OR (radii)
PO = PO (common side)
∠PQO = ∠PRO (Right angle)
Hence; Î” POQ â‰ˆ Î” POR proved
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