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 cmB. 3 cmC. 4 cmD. 5 cm

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

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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