Share

Books Shortlist

# In the Given Figure, Chord Ed is Parallel to Diameter Ac of the Circle. Given ∠Cbe = 65°, Calculate ∠Dec. - ICSE Class 10 - Mathematics

ConceptArc and Chord Properties - the Angle that an Arc of a Circle Subtends at the Center is Double that Which It Subtends at Any Point on the Remaining Part of the Circle

#### Question

In the given figure, chord ED is parallel to diameter AC of the circle. Given ∠CBE = 65°, calculate ∠DEC.

#### Solution

Join OE.
Arc EC subtends ∠EOC at the centre and ∠EBC at the remaining Part of the circle.
∠EOC = 2 ∠EBC = 2 ×65° =130°

Now in ΔOEC, OE = OC      [radii of the same circle]

∴ ∠OEC = ∠OCE
But, in ΔEOC ,
∠OEC + ∠OCE + ∠EOC = 180° [Angles of a triangle]
⇒  ∠OCE + ∠OCE + ∠EOC = 180°
⇒ 2 ∠OCE + 130° = 180°
⇒ 2 ∠OCE = 180° -130°
⇒ 2 ∠OCE = 50°
 ∠OCE = (50°)/2 = 25°
∴ AC || ED          [Given]

∴ ∠DEC = ∠OCE
⇒ ∠DEC = 25°

Is there an error in this question or solution?

#### Video TutorialsVIEW ALL [1]

Solution In the Given Figure, Chord Ed is Parallel to Diameter Ac of the Circle. Given ∠Cbe = 65°, Calculate ∠Dec. Concept: Arc and Chord Properties - the Angle that an Arc of a Circle Subtends at the Center is Double that Which It Subtends at Any Point on the Remaining Part of the Circle.
S