In the given figure, O is the centre and AB is a diameter of the circle AC and - Maths - Triangles

Question

In   the   given   figure ,   O   is
  the   centre   and   AB   is   a
  diameter   of   the   circle     AC
  and   BD   when   produced   ,  
meet   at   E If   ∠ COD   =   50
°   ,   then   ∠ CED =    
                 
              ?

1   100 °           2   65
°           3   130 °  
      4   None   of   these

Lovina Kansal · Accepted Answer

Dear student
Given:∠COD=50°Clearly,∠CBD=12×∠COD=25°     [Prove that the angle subtended by an arc of a circle at the centre is double the angle subtended by it at any point on the remaining part of the circle
]Since ∠ACB is angle is a semi-circle
∴∠ACB=90°⇒∠BCE=180°-∠ACB=180°-90°=90°Thus, in △BCE, we have∠BCE=90 and ∠CBE=∠CBD=25°∴∠BCE+∠CBE+∠CEB=180°⇒90°+25°+∠CEB=180°⇒∠CEB=65°
Regards

In the given figure , O is the centre and AB is a diameter of the circle . AC and BD when produced , meet at E . If ∠ COD = 50 ° , then ∠ CED = ? 1 100 ° 2 65 ° 3 130 ° 4 None of these .

$In the given figure, O is the centre and AB is a diameter of the circle . AC and BD when produced, meet at E . If ∠ COD = 50 °, then ∠ CED = ?$

$(1) 100 ° (2) 65 ° (3) 130 ° (4) None of these .$