Proof: Radius is Perpendicular to Tangent of a Circle | Geometry

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We prove the well known, and very useful, result that the radius of a circle is perpendicular to the tangent that intersects it at a single point on the circle. To do this, we use a really neat contradiction argument, producing a point on our tangent line that will cause some serious trouble! #Geometry

How could you prove the converse? That if a radius meets a line at a point on a circle at a right angle, then the line is a tangent?

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Комментарии
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You explained each step of this proof so logically and with such clarity!! This is so helpful for my exams!! Thank you

diyabhat
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When you claim that in the segment OQ there's a point R, that belongs to the circumference, tacitly you are supposing that OQ is grater than the radius of the circle.

henryleon
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op is the radius and OQ clearly indicates the distance from the center of the circle to a point outside of the circle means it must be greater than the radius OP. So, OP<OQ. Your explanations are counterintuitive and seems incoherent to me.

rayhanalam