Question

prove that the prependicular at the point of contact to the tangent to a circle passes through the centre

Answer 1

Step-by-step explanation:

Let O be the centre of the given circle.

AB is the tangent drawn touching the circle at A.

Draw AC ⊥ AB at point A, such that point C lies on the given circle.

∠OAB = 90° (Radius of the circle is perpendicular to the tangent)

Given ∠CAB  = 90°  

∴ ∠OAB = ∠CAB

This is possible only when centre O lies on the line AC.

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

Answer 2

Brainly.in

What is your question?

rarvs123

Secondary SchoolMath 5+3 pts

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

Report by Adhaliwal7430 20.01.2018

Answers

Róunak

Róunak Maths AryaBhatta

Hey mate ...

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|| Due to some network issues, I cannot post the pic. ||

Soln--->

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.

Hope it helps!!