Prove that the perpendicular at the point of contact to the tangent to

1.	Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.
Answer» Step-by-step explanation: O is the centre of the given circle.(draw any ) A tangent PR has been drawn touching the circle at point P. Draw QP ⊥ RP at point P, such that point Q LIES on the circle. ∠OPR = 90° (radius ⊥ tangent) ALSO, ∠QPR = 90° (Given) ∴ ∠OPR = ∠QPR Now, above case is possible only when centre O lies on the line QP. Hence, PERPENDICULAR at the point of CONTACT to the tangent to a circle passes through the centre of the circle.

Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.

Answer»

Step-by-step explanation:

O is the centre of the given circle.(draw any )

A tangent PR has been drawn touching the circle at point P.

Draw QP ⊥ RP at point P, such that point Q LIES on the circle.

∠OPR = 90° (radius ⊥ tangent)

ALSO, ∠QPR = 90° (Given)

∴ ∠OPR = ∠QPR

Now, above case is possible only when centre O lies on the line QP.

Hence, PERPENDICULAR at the point of CONTACT to the tangent to a circle passes through the centre of the circle.

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

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Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.