Question

prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre​

Answer 1

Step-by-step explanation:

Given a circle with center O and AB the tangent intersecting circle at point P

and prove that OP⊥AB

We know that tangent of the circle is perpendicular to radius at points of contact Hence

OP⊥AB

So, ∠OPB=90 -1

Now lets assume some point X

Such that XP⊥AN

Hence ∠XPB=90 -2

From eq (i) & (ii)

∠OPB=∠XPB=90

Which is possible only if line XP passes though O

Hence perpendicular to tangent passes though centre

Answer 2

Answer:

here's explanation in attachment