Question

In the given figure, two radii OA and OB of a circle with centre 'O' are perpendicular to each other. If two tangents drawn at points A and B intersect each other at point T, prove that $AB = OT$ and they bisect each other.

Circle with perpendicular radii OA and OB and intersecting tangents at T

Accepted Answer

In quadrilateral OATB: $\angle AOB = 90^\circ$, and $\angle OAT = \angle OBT = 90^\circ$ (radius $\perp$ tangent). Hence OATB is a rectangle with adjacent sides $OA = OB = r$, making OATB a square. Since diagonals of a square are equal and bisect each other, $AB = OT$ and they bisect each other.

Tangents from perpendicular radii

Explanation

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