If a hexagon PQRSTU circumscribes a circle, prove that, PQ + RS + TU = QR + ST + UP

CBSE Class 10 Maths PYQ · Circles · Hexagon & Circle · 3 Marks · March 2024 · Standard

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1313 Marks · March 2024 · Standard

If a hexagon PQRSTU circumscribes a circle, prove that,
PQ + RS + TU = QR + ST + UP

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Correct figure
In the given figure,
PA = PF ... (1)
AQ = BQ ... (2)
RC = RB ... (3)
CS = DS ... (4)
ET = TD ... (5)
UE = UF ... (6)
Adding (1), (2),(3), (4), (5) and (6),
PA + AQ + RC + CS + ET + UE = PF + BQ + BR + DS + TD + UF
$\Rightarrow$ PQ+RS+TU = UP+ST+QR