In the given figure, if AB = AC, ∠ACD is an obtuse angle, and E is the mid-point of AC, then which of the following is always correct?

2ED > 3CD

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2ED > AB

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

BC > 2AB

No worries! We‘ve got your back. Try BYJU‘S free classes today!

AC > ED + EC

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B 2ED > AB
Given that AB = AC and E is mid-point of AC.
∴ AC = AB = 2EC
Since ∠ACD is an obtuse angle
∴ ED > EC (Side opposite to the largest angle is the longest)
⇒ 2ED > 2EC (Multiplying both sides by 2)
⇒ 2ED > AB (∵ AB = 2EC)
Hence, the correct answer is option (b).

Suggest Corrections

Similar questions

Q. In the given figure, B is an obtuse angle, if M and N are the mid-points of AB and AC respectively, then AN is always greater than

In the figure, $△ A B C$ is an isosceles triangle in which AB = AC. If D and E are the mid-points of sides AB and AC respectively and $∠ D O E = 120^{\circ}$ , then find $∠ O D E$ .

Q. In the given figure, AD is bisector of

∠

A and AB

=

AC. Then

Δ

ACD,

Δ

ABD are congruent by which criterion?

Q. In the given figure, AB = AC, BN and CM are bisectors of ∠ABC and ∠ACB respectively. If AB and AC are the bisectors of ∠MAO and ∠OAN respectively, then which of the following is always correct?

In the given figure AD is the bisector of $∠$ A and AB = AC. Then, by which criterion $△$ ACD and $△$ ABD are congruent?

Join BYJU'S Learning Program