Question

प्रूव दैट द परपेंडिकुलर राइट द पॉइंट ऑफ कांटेक्ट टू द चेंज इन टू अ सर्कल पासेस थ्रू द सेंटर​

Answer 1

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

o

..........(i)

Now lets assume some point X

Such that XP⊥AN

Hence ∠XPB=90

o

.........(ii)

From eq (i) & (ii)

∠OPB=∠XPB=90

o

Which is possible only if line XP passes though O

Hence perpendicular to tangent passes though centre