# In the Adjoining Figure O is the Centre of the Circle Whose Diameter is Mn. Measures of Some Central Angles Are Given in the Figure. - Mathematics

Sum

In the adjoining figure O is the centre of the circle whose diameter is MN. Measures of some central angles are given in the figure. hence find the following.

(1) m∠ AOB and m∠ COD
(2) Show that arc AB ≌ arc CD.
(3) Show that chord AB ≌ chord CD

#### Solution

(1) MN is the diameter of the circle with centre O.

∠MOA + ∠AOB + ∠BON = 180°

⇒ 100° + ∠AOB + 35° = 180°

⇒ ∠AOB = 180° - 100° - 35° = 45°

Similarly, ∠COD = 45°

(2) Eqaual arcs subtend equal angles at the centre.

∠AOB = ∠COD = 45°

So, arc AB ≌ arc CD
(3) Corresponding chords of congruent arcs are congruent.

arc AB ≌ arc CD
So, chord AB ≌ chord CD

Concept: Arcs Corresponding to the Chord of a Circle
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Chapter 17: Circle : Chord and Arc - Practice Set 17.2 [Page 118]

#### APPEARS IN

Balbharati Mathematics 8th Standard Maharashtra State Board
Chapter 17 Circle : Chord and Arc
Practice Set 17.2 | Q 2 | Page 118
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