Q. 205.0( 1 Vote )

In Fig. 10.142, if AC is bisector of BAD such that AB=3 cm and AC=5 cm, then CD=


A. 2 cm

B. 3 cm

C. 4 cm

D. 5 cm

Answer :

In using Pythagoras theorem, we get

AB2 + BC2 = AC2


9 + BC2 = 25


BC = 4 cm


In


BAC = CAD (Therefore, AC is bisector of A)


B = D = 90o


ABC + BCA + CAB = 180o


CAD + ADC + DCA = 180o


ABC + BCA + CAB = CAD + ADC + DCA


BCA = DCA (i)


In


CAB = CAD (Therefore, AC is bisector of A)


BCA = DCA [From (i)


AC = AC (Common)


By ASA theorem, we have



BC = CD (By c.p.c.t)


CD = 4cm

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