Let's draw a tangent PQ to a circle as shown below.
Let's draw a tangent PQ to a circle as shown below.Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre
Let's draw a tangent PQ to a circle as shown below.Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centreAs we know that, a tangent at any point of a circle is perpendicular to the radius through the point of contact.
Let's draw a tangent PQ to a circle as shown below.Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centreAs we know that, a tangent at any point of a circle is perpendicular to the radius through the point of contact.At the point of contact P, RP is perpendicular to the tangent PQ.
Let's draw a tangent PQ to a circle as shown below.Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centreAs we know that, a tangent at any point of a circle is perpendicular to the radius through the point of contact.At the point of contact P, RP is perpendicular to the tangent PQ.We also know that the radius or diameter will always pass through the centre of the circle.
Let's draw a tangent PQ to a circle as shown below.Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centreAs we know that, a tangent at any point of a circle is perpendicular to the radius through the point of contact.At the point of contact P, RP is perpendicular to the tangent PQ.We also know that the radius or diameter will always pass through the centre of the circle.Therefore, PR passes through the centre O.
Let's draw a tangent PQ to a circle as shown below.Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centreAs we know that, a tangent at any point of a circle is perpendicular to the radius through the point of contact.At the point of contact P, RP is perpendicular to the tangent PQ.We also know that the radius or diameter will always pass through the centre of the circle.Therefore, PR passes through the centre O.Hence it is proved that perpendicular PR of tangent PQ passes through centre
Answers & Comments
Verified answer
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
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
Let's draw a tangent PQ to a circle as shown below.
Let's draw a tangent PQ to a circle as shown below.Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre
Let's draw a tangent PQ to a circle as shown below.Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centreAs we know that, a tangent at any point of a circle is perpendicular to the radius through the point of contact.
Let's draw a tangent PQ to a circle as shown below.Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centreAs we know that, a tangent at any point of a circle is perpendicular to the radius through the point of contact.At the point of contact P, RP is perpendicular to the tangent PQ.
Let's draw a tangent PQ to a circle as shown below.Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centreAs we know that, a tangent at any point of a circle is perpendicular to the radius through the point of contact.At the point of contact P, RP is perpendicular to the tangent PQ.We also know that the radius or diameter will always pass through the centre of the circle.
Let's draw a tangent PQ to a circle as shown below.Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centreAs we know that, a tangent at any point of a circle is perpendicular to the radius through the point of contact.At the point of contact P, RP is perpendicular to the tangent PQ.We also know that the radius or diameter will always pass through the centre of the circle.Therefore, PR passes through the centre O.
Let's draw a tangent PQ to a circle as shown below.Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centreAs we know that, a tangent at any point of a circle is perpendicular to the radius through the point of contact.At the point of contact P, RP is perpendicular to the tangent PQ.We also know that the radius or diameter will always pass through the centre of the circle.Therefore, PR passes through the centre O.Hence it is proved that perpendicular PR of tangent PQ passes through centre