Book Online Demo

Check Your IQ

Try Test

Courses

Offline Centres

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

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

2:3

4:5

2:5

None of these

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

In rectangle ABCD Given that,

A B = 25

cm and BC = 15cm.
Question Image

Since, CO is the bisector of

∠ C

that divides AB.

∴ ∠ O C B = ∠ O C D = 45 ° ........................ (1)

Δ O C B

using angle sum property:

∠ C B O + ∠ O C B + ∠ C O B = 180 ° 90 ° + 45 ° + ∠ C O B = 180 ° ∠ C O B = 180 ° − (90 ° + 45 °) ∠ C O B = 180 ° − (135 °) ∠ C O B = 45 ° ..................... (2)

From equation (1) and (2),

∠ O C B = ∠ C O B O B = B C ⇒ O B = 15 c m

[sides to opposite to the equal angles are also equal]
And finding side AO,

25 − x = O B x = 25 − O B x = 25 − 15 x = 10 c m

Thus AO= 10cm.
Now the ratio by which CO divides AB is AO: OB.
So ratio,

\frac{10}{15} = \frac{2}{3}

Hence, option 1 is correct.

Watch 3-min video & get full concept clarity

JEE

NEET

Foundation JEE

Foundation NEET

CBSE