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Why does the construction of a tangent at a point P on a circle by drawing an arc centred at P and joining intersection points with the circle work as designed?
Answer & Solution
Correct answer: D.
1. The arc centred at P meets the circle in two symmetric points relative to P.
2. The triangle formed by these two points and any third point on the circle has equal base angles.
3. The line through P parallel to the base of that isosceles triangle is the tangent at P.
4. This relies on the equal-base-angle property of the isosceles construction rather than any centre information.
5. The construction does not locate the centre directly, and the chord drawn is not itself the tangent.
_Source: SCERT Kerala Std X Mathematics Part-2, Chapter 7 "Tangents" (pp 159-172, 2019 ed.)._
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