Question

A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB+CD =AD+BC.

Answer 1

Answer:

Step-by-step

PROVE THAT:AB+CD=AD+BC

PROOF:

AP=AS  -----1

PB=BQ  -----2      [TANGENTS DRAWN FROM

CR=CQ  -----3       EXTERNAL POINTS ARE

DR=DS   -----4            EQUAL]

                          AB+CD= AP+PB+CR+DR  [FROM FIG]

                                         = AS+BQ+CQ+DS   [FROM 1,2,3,4]

                                         = (AS+DS)+(BQ+CQ)

                                         = AD+BC