alleryIn a quadrilateral ABCD circumscribed about a circle, AB + CD equals
AAC + BD
BAD - BC
CAD + BC
D2 AB
Answer & Solution
Correct answer: C. AD + BC
1. Each pair of tangent segments from a vertex is equal.
2. AB + CD = (AP + PB) + (CR + RD); AD + BC = (AS + SD) + (BQ + QC). Both equal sum of all tangent halves.
3. Hence AB + CD = AD + BC.
_Source: syllabus Mathematics, Ch 10 "Circles", §10.3_
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