The size of the angle DOA is 68°
What is the tangent of the circle?
"It is the line which intersects the circle exactly at one point."
For given example,
BC and AC are tangents to the circle.
∠OCB = 34°
As, OC is the angle bisector for ∠ACB
⇒ ∠OCB = ∠OCA
⇒ ∠OCA = 34°
⇒ ∠ACB = ∠OCB + ∠OCA
⇒ ∠ACB = 34° + 34°
⇒ ∠ACB = 68°
We know, the tangent to a circle is perpendicular to the radius of the circle.
⇒ CB ⊥ OB
⇒ ∠OBC = 90°
and CA ⊥ OA
⇒ ∠OAC = 90°
We know, the sum of all angles of quadrilateral is 360°.
For quadrilateral ACBO,
⇒ ∠OAC + ∠ACB + ∠OBC + ∠BOA = 360°
⇒ 90° + 68° + 90° + ∠BOA = 360°
⇒ ∠BOA = 112°
We know, the angle subtended by semicircle is 180°.
⇒ ∠AOB + ∠DOA = 180°
⇒ 112° + ∠DOA = 180°
⇒ ∠DOA = 68°
Therefore, the size of the angle DOA is 68°
Learn more about the tangents of the circle here:
https://brainly.com/question/23265136
#SPJ2
