A quadrilateral $ABCD$ is drawn to circumscribe a circle. Prove that $AB + CD = AD + BC$.
Step-by-Step Solution
Key Concept: Tangents from external point: $AP = AS, BP = BQ, CR = CQ, DR = DS$. Add all 4 equations.
Tangents from external points: $AP = AS$, $BP = BQ$, $CR = CQ$, $DR = DS$. [1.0 Mark]
Add equations: $(AP + BP) + (CR + DR) = (AS + DS) + (BQ + CQ) \Rightarrow AB + CD = AD + BC$. Proved! [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Writing 4 tangent equalities: 1.0 Mark
Adding equations to conclude $AB + CD = AD + BC$: 1.0 Mark
Correct Answer: