Question

In the following figure, ED = EC. Then, which of the options is/are true?

• A. 180°
• B. 360°
• C. 90°
• D. 270°

Answer 1

Answer: (B), (D)

The correct options are
B

360°

D

270°

$BE<BD\Rightarrow BE<BD+EC$

So, option (a) is not correct.

In $\Delta ADB$,

$AB+AD>BD$ [Sum of any two sides is always greater than the third]

$\Rightarrow AB+AD>BE+ED$

$\Rightarrow AB+AD>BE+EC[EC=ED]\dots \dots \left(1\right)$

Also in $\Delta BEC$, $BE+EC>BC\dots \dots \left(2\right)$

From (1) and (2), BC < AB + AD

So, option (b) is correct.

$BD=BE+EC=BE+ED[EC=ED]$

Option (c) is not correct.

In $\Delta BEC$, $BE>BC-EC$ [Difference of any two sides is always less than the third]

$\Rightarrow BE+EC>BC$

$\Rightarrow BE+ED>BC[EC=ED]$

$\Rightarrow BD>BC$

So, option (d) is correct.

$\therefore$ b and d are correct options.