ICSE Class 10CISCE
Share
Notifications

View all notifications
Books Shortlist
Your shortlist is empty

In the Figure Given Below, Ab is Diameter of the Circle Whose Centre is O. Given That: ∠Ecd = ∠Edc = 32°. Show that ∠Cof = ∠Cef. - ICSE Class 10 - Mathematics

Login
Create free account


      Forgot password?
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 figure given below, AB is diameter of the circle whose centre is O. given that: ∠ECD =
∠EDC = 32°. Show that ∠COF = ∠CEF.

Solution

Here, ∠COF = 2 ∠CDF = 2 × 32° = 64°  ……… (i)
(Angle at the centre is double the angle at the circumference subtended by the same chord)
In ΔECD,
∠CEF = ∠ECD +∠EDC = 32° +32°  = 64°  ………….(ii)
(Exterior angle of a Δ is equal to the sum of pair of interior opposite angles)
From (i) and (ii), we get
∠COF =∠CEF

  Is there an error in this question or solution?
Solution In the Figure Given Below, Ab is Diameter of the Circle Whose Centre is O. Given That: ∠Ecd = ∠Edc = 32°. Show that ∠Cof = ∠Cef. 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
View in app×