Question

4. In a circle with centre O and a chord BC, Points D and E lie on the same side
of BC. If L BDC = 80°, then L BEC=
a) 20°
b) 80°
c) 160°
d) 40°​

Answer 1

Explanation:

Given:

In a circle with centre O and a chord BC, Points D and E lie on the same side of BC.  

Find:

∠BDC=80°, ∠BEC=?

Solution:

• An circle is centre O.

• A chord is BC.

• Points D and E.

• E lie on the same side of BC.

• ∠BDC=80° Then find the value of, ∠BEC=?

Here ∠BEC is 2 times of ∠BDC

∠BEC=2∠BDC

Now, Substitute the value of ∠BDC=80°

2 ∠BDC =2 ×80°

Then Multiply the numbers:

= 2×80°

=160°

Hence,

Answer is 160°

Hence , The option (c) 160° is correct.

Answer 2

∠BEC = 80° if in a circle with centre O and a chord BC, Points D and E lie on the same side of BC and ∠BDC = 80°

Given:

A circle with center O

Chord BC

Points D and E lie on the same side of BC

∠BDC = 80°

To Find:

∠BEC

An inscribed angle is an angle whose sides contain chords of a circle with a common endpoint.

In a circle, if two inscribed angles intercept the same arc, then they are congruent.

or Angles formed by a chord on same sides of chord in circle are of Equal measures

Step 1:

As Point D and E are on same sides of chord BC

Hence ∠BDC = ∠BEC

Step 2:

Substitute ∠BDC = 80°

80° = ∠BEC

Hence,  ∠BEC = 80°

Correct option is b) 80°

Additional information:

∠BOC = 2∠BDC = 2∠BEC

∠BOC = 2 (80°) = 160°