CBSE Class 9 Answered
Prove that quadrilateral formed (if
possible) by the internal angle bisectors of any quadrilateral is cyclic.
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
Expert Answer
AH, BF, CF and DH are bisectors of A, B, C and D respectively which form quadrilateral EFGH.
FEH = AEB = 180o - EAB - EBA (angles of AEB)
= 180o - (A + B)
FGH = DGC = 180o - GDC - GCD (angles of DGC)
= 180o - (D + C)
FEH + FGH = 180o -
EFGH is a cyclic quadrilateral
(If the sum of a pair of opposite angles of a quadrilateral is 180º, then the quadrilateral is cyclic)
Answered by | 04 Jun, 2014, 03:23: PM
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