Question

in the figure 'o' is the centre of the circle and AB,CD are equal chords. if angle AOB=70 find the angels of the triangle OCD

Answer 1

55°,70°,55° are the angle measurements

Answer 2

Answer:

Step-by-step explanation:

In ΔAOB, AO=OB=x (Radius of circle), therefore, angles made by them will also be equal.

Therefore, using the angle sum property,

∠BAO+∠AOB+∠OBA=180°

x+x+70°=180°

2x=110°

x=55°

AS, AB and CD are the two chords of the circle, AB=CD

From ΔODC and ΔAOB,

OD=OA(radius of circle)

∠ODC=∠AOB=70°(vertically opposite angles)

OB=OC(radius of circle)

By SAS rule,

ΔODC ≅ ΔAOB⇒ All angles will be equal.

Thus, ∠BAO=∠ABO=∠ODC=∠OCD=55°

Therefore, in ΔODC,

∠ODC=∠OCD=55° and ∠DOC=70°