u uiuincaCcle aie paraliel.S. Pove that the perpearen octhrough the ce

1.	u uiuincaCcle aie paraliel.S. Pove that the perpearen octhrough the centre.
Answer» Let , O is the centre of the given circle. 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.

u uiuincaCcle aie paraliel.S. Pove that the perpearen octhrough the centre.

Answer»

Let ,

O is the centre of the given circle.

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.