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Question 135
In a rectangle ABCD, AB = 25 cm and BC = 15 cm. In what ratio, does the bisector of C divide AB?


Solution

Given, AB = 25 cm and BC = 15 cm
Now, in rectangle ABCD,

CO is the bisector of C and it divides AB.
OCB=OCD=45

In ΔOCB,
CBO+OCB+COB=180    [angle sum property of triangle]
90+45+COB=180COB=180(90+45)COB=180135=45

Now, in ΔOCB,
OCB=COB
Then, OB = BC
OB=15 cm
AO=25OB=2515=10 cm
CO divides AB in the ratio AO : OB
CO divides AB in the ratio: 10:15=2:3

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