Segment formed by a point inside a circle and a point outside intersects the circle?

Asked Apr 29 '21 at 16:18

Active Apr 29 '21 at 16:31

Viewed 26 times

O is the center of the circle of radius r. We have two points A and B | OA < r and OB > r. I have to prove that AB intercepts the circle. I tried to use the line segment that contains AB to build a perpendicular line that intercepts O, the point of intersection of these two lines I called C. So I formed 2 right triangles, OCA and OCB. I tried to use the Pythagorean theorem, but I cannot relate these triangles to find the point of intersection of the line segment that contais AB with the circle.

Can someone help me? Sorry for my bad English, I don't know much of that language

edited Apr 29 '21 at 16:31

asked Apr 29 '21 at 16:18

Wesley

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What is the meaning of "| OA r." in the first line ? – Jean Marie Apr 29 '21 at 16:21
You have to prove it by pure geometry or analytical (coordinates) geometry ? – Jean Marie Apr 29 '21 at 16:22
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The proof depends strongly on the axiomatic system that describes the geometry. Please specify a bit about it. – ajotatxe Apr 29 '21 at 16:23
Such that the OA line segment is smaller than the radius of the circle. Pure geometry, using the axioms of Euclidean geometry – Wesley Apr 29 '21 at 16:30

Segment formed by a point inside a circle and a point outside intersects the circle?

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