A tangent is perpendicular to the radius which starts from the center of circle and touches the point where the tangent intersects the circle
Thus:
No, it is not possible for tangents intersecting a circle at opposite endpoints of same diameter to intersect.
Short reason is because they must be parallel. Explanation is shown below.
It is known that:
Two tangents are there on a circle such that they intersect the circle at opposite endpoints of same diameter of the circle.
To find:
Whether both tangents are intersecting each other or not.
How to know if the tangents are intersecting each other?
The diagram is shown below.
There is a theorem which states that:
"A tangent is perpendicular to the radius which starts from the center of circle and touches the point where the tangent intersects the circle"
Thus, we have both tangents perpendicular to the common diameter which has got two opposite radii, touching intersection points of the tangents.
Since both the tangents are perpendicular to same line thus they must be parallel to each other.
Thus, No, it is not possible for tangents intersecting a circle at opposite endpoints of same diameter to intersect.
Learn more about tangents here:
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