Math, asked by skb97, 1 year ago

prove that the perpendicular at any point of contact to the tangent to a circle passes through the center​

Answers

Answered by aarvi46
0

Step-by-step explanation:

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.

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Answered by TanikaWaddle
3

Given :Let us assume a circle with center O and AB be the tangent intersecting circle at point P

To prove : OP ⊥AB

proof :

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

OP ⊥AB

So ∠OPB = 90°

noe let us assume a point X

such that XP⊥ AB

∠XPB = 90°..(2)

From 1 and 2

∠OPB  =∠XPB = 90°

which is possible if the line XP passes through O

hence , perpendicular to the tangent to a circle passes through the center​

#Learn more :

https://brainly.in/question/12480022

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