Question

a circle inscribed a quadrilateral ABCD in whichAD = 23 cm ,AB = 29 cm and DC= 15 cm find the side BC

Answer 1

  Given: AB=30cm AD=24 cm DS= 8 cm   (let here S = G,) To find: r solution: 1) AH=AE 2) DG = DH                              ( tangents from an external point are equal) 3) CG  = CF4)BE=BF let O be the centre of the circlejoin O to E and O to F thus we can say that OEBF   is a square.(angle B=900,BE=BF, OE=OF{radii} ) now, 5)DH=DG=8 cmAD=24 AH=24-8 AH= 16 cm from equation 1, AE= 16 cm now, AB= 30 cmBE = 30-16 BE=14 cm since we know that OEBF is a square, all sides will be equaltherefore, OE=OF=BE=BF= 14 CMtherefore radius of circle is 14cm