Question

O is the centre of the circle. If chord AB = chord CD,
then find x.​

Answer 1

Answer:

The value of x = 55

Step-by-step explanation:

Given,

O is the centre of the circle

Chord AB = Chord CD

To find,

The value of 'x'

Recall the concept

Vertically opposite angles are equal

The sum of three angles of a triangle is equal to 180 degrees

The base angles of an isosceles triangle are equal.

Solution:

∠AOB and ∠COD are vertically opposite angles.

Since vertically opposite angles are equal, we have

∠AOB = ∠COD

Since ∠AOB = 70, we have ∠COD  = 70

In Δ COD, we have  CO and DO  are the radii of the circle.

Since the radii of the circle are equal, we have CO = DO

Then Δ COD is an isosceles triangle,  the base angles of an isosceles are  equal

∠OCD = ∠ODC

Since ∠OCD = x, then ∠ODC = x

Sum of three angles of triangle is 180 degrees

∠OCD +∠ODC + ∠COD = 180

x+x+70 = 180

70 +2x = 180

2x = 180 -70

2x = 110

x = 55

∴The value of x = 55

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Answer 2

Answer:

The value of x is 55°.

Step-by-step explanation:

Given: O is the centre of the circle in which chord AB = chord CD.

To find: The value x.

From the figure,

Since AB = CD

⇒ ∠COD = ∠AOB (The congruent chords subtend congruent angles)

⇒ ∠COD = 70°

Also,

OD = OC (Being the radii of the circle)

⇒ ΔCOD is an isosceles triangle

⇒ ∠ODC = ∠OCD (Angles opposite to equal sides are equal)

⇒ ∠ODC = x (Since ∠OCD = x)

Now,

In ΔCOD,

∠OCD + ∠ODC + ∠COD = 180° (Angle sum property)

                      x $+$ x $+$ 70° = 180°

                                   2x = 180° - 70°

                                   2x = 110°

                                     x = 55°

Therefore, the value of x is 55°.

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