Question

a tangent to a circle is perpendicular to the radius through the point of the contact

Answer 1

Given, circle with centre O and radius r.
Tangent XY at point of contact P
To Prove → OP Perpendicular to XY

Construction→ Let Q be a point on XY. Join OQ. Let it intersect circle at R.

Proof → By construction,

OQ > OR

OR = OP (radii of same circle)

OQ > OP

For all the points on tangent XY, OP will be the smallest.
The smallest length is Perpendicular.
Hence OP Perpendicular to XY

Answer 2

Answer:

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