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Tangents drawn to a circle at the four endpoints of a pair of perpendicular chords form a quadrilateral. This quadrilateral is always:
Answer & Solution
Correct answer: C.
1. Each angle at an external vertex of the new quadrilateral equals 180° minus the central angle of the corresponding chord.
2. The two perpendicular chords produce two central angles whose sum equals 180° at the centre.
3. So the two opposite angles of the tangent quadrilateral together equal 180°, satisfying the cyclic condition.
4. The quadrilateral is therefore cyclic regardless of the lengths of the chords.
5. It is a square only in the special case of two diameters that are perpendicular.
_Source: SCERT Kerala Std X Mathematics Part-2, Chapter 7 "Tangents" (pp 159-172, 2019 ed.)._
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