If a regular hexagon ABCDEF circumscribes a circle, then prove that AB + CD + EF = BC + DE + FA .

CBSE Class 10 Maths PYQ · Circles · Quad & Circle · 3 Marks · March 2026 · Standard

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1253 Marks · March 2026 · Standard

If a regular hexagon ABCDEF circumscribes a circle, then prove that $AB + CD + EF = BC + DE + FA$.

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correct figure (1/2 Mark)
AM = AR
BM=BN
CN = CO
DO = DP
EQ=EP
FQ=FR (1 Mark)
LHS $= AB+CD+EF = (AM+BM) + (CO+OD) + (EQ + QF)$ (1/2 Mark)
$= AR+ BN + CN + DP + EP + FR$ (1/2 Mark)
$= (AR+FR) + (BN+CN)+ (DP+EP)$ (1/2 Mark)
$= BC + DE+ FA = \text{RHS}$