Question

ABCD is a cyclic quadrilateral inscribed in a circle of radius 5. E is a point on the arc ADC. If angle AEC is 20° then
1) angle ABC is 160°
2) angle ADC is 20°
3) angle ABC is 100°
4) angle ADC is 100°

Answer 1

Answer:

Option A & B are Correct.

Step-by-step explanation:

Given: ABCD is cyclic Quadrilateral in circle with centre O

           ∠AEC = 20°

Figure is attached.

E is on circle

⇒ AECB is also Cyclic Quadrilateral.

We know that Sum of opposite angles of cyclic quadrilateral is 180°

in cyclic Quadrilateral AECB

∠AEC + ∠ABC = 180°

20° + ∠ABC= 180°

∠ABC = 180 - 20

∠ABC = 160°

Thus, Option A is correct.

CD is chord to circle of radius O

Using Result which states that.

Angle subtended by same chord in same segment are equal.

we get,

∠ADC = ∠AEC = 20°

Thus, Option B is correct.

Therefore, Option A & B are Correct.