MathematicsIf the chord of a circle is equal to its radius, then which of the following is the angle subtended by this chord at the minor arc of the circle?

If the chord of a circle is equal to its radius, then which of the following is the angle subtended by this chord at the minor arc of the circle?


  1. A
    150°
  2. B
    130°
  3. C
    120°
  4. D
    110° 

    Fill Out the Form for Expert Academic Guidance!l



    +91



    Live ClassesBooksTest SeriesSelf Learning



    Verify OTP Code (required)

    I agree to the terms and conditions and privacy policy.

    Solution:

    Given,
    AB is the chord equal to the radius. OA and OB are the radii of the circle. ADB is the minor arc, and ACB is the major arc. OA = OB = AB       …(since AB is equal to radius). So, AOB is an equilateral triangle as all sides are equal. ⇒∠AOB=∠OAB=∠OBA=60°.
    Angle subtended by the chord AB at the minor arc of the circle is ∠ADB.
    ⇒reflex∠AOB=360°-∠AOB
    ⇒reflex∠AOB=360°-60°
    ⇒reflex∠AOB=300°
    ⇒reflex∠AOB=2×∠ADB
    ⇒300°=2×∠ADB
    ⇒∠ADB=300°2
    ⇒∠ADB=150°
    Hence, the angle subtended by this chord at the minor arc of the circle is 150°. Therefore, option 1 is correct.
     
    Chat on WhatsApp Call Infinity Learn