Question

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

Answer 1

Answer:

Given, AB = 25cm and BC = 15cm

Step-by-step explanation:

Now, in rectangle ABCD,

Co is the bisector of angle C and it divides AB.

angle OCB = angle OCD = 45°

angle OCB = angle OCD = 45°

In triangle OCB, we have,

angle CBO + angle OCB + angle BOC = 180°

[ angle sum property of triangle]

90° + 45° + angle BOC = 180°

135° + angle BOC = 180°

angle BOC = 180° - 135° = 45°

now, in triangle OCB,

angle OCB = angle BOC

OB = BC

OB = 15cm

CO divides AB in the ratio AO : OB

Let AO be x , then

OB = AB - x

OB = 25 - x

AO : OB = x : 25 - x

10 : 15

2:3