Question

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

Answer 1

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. ... Hence, perpendicular at the point of contact to the tangent to a circle passes through the centre of the circle.

Step-by-step explanation:

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Answer 2

Given :- AB is a tangent to the circle with centre O at the point P and D P perpendicular to AB

T.P :- DP passes through O

Proof :- let us take a point X such that XP perpendicular to AB

= angle XPB = 90°

we know that, radius is a perpendicular to the tangent at the point of contact

= XP should be radius .

= X should lie on OP

Thus, we can say it for D also as DP perpendicular to AB

= angle DPB =90°

= D should also lie on OP

so DP passes through OP