Question

3. prove that the tangents brown a perpendicula, at the point
of contact to the tangent to a corto passes through the
centro​

Answer 1

Answer:

Given: Let us assume a circle with centre O & AB be the tangent intersecting circle at point P.

To prove: OP⊥ AB

Proof: We know that

Tangent of circle is $$\perpendicular to radius at point of contact.

Hence, OP⊥AB(Tangent at any point of circle is perpendicular to the radius through point of contact)

So, ∠OPB=90

o

……….(1)

Now, lets assume some point x, such that XP⊥AB

Hence, ∠XPB=90

o

……….(2)

From (1) & (2)

∠OPB=angleXPB=90

o

which is possible only if line XP passes through.

Hence, perpendicular to tangent passes through centre.

solution