Answer:
Step-by-step explanation:
Here we are going to use the rule which says that
i) equal arc segments subtends equal angles at the circle
ii) The Angle subtended by any arc segment at center is double to that of the angle subtended by the same arc at its circumference.
For more details please refer to the image attached to this problem.
Let us say that the angle subtended by arc mAB at center O = 6∅
Hence , ∠AOB=6∅
Hence ∠ADB = 3∅ ( Rule ii as discussed above )
Also as length of arc mCD = x , the angle subtended by it on the center will be in the same ratio as it was subtended by arc with length 6x
Hence
∠COD=∅
Hence
∠CAD=∅/2
Hence in ΔATD
∠ATD + ∠ADT +∠DAT = 180°
∠ATD + 3∅+∅/2= 180°
∠ATD = 180° - (3∅+∅/2) ----------(A)
Also
∠ATD + ∠ATB = 180°
From (A)
180° - (3∅+∅/2) +∠ATB = 180°
∠ATB = (3∅+∅/2)
∠ATB = (6∅+∅)/2
∠ATB = (7∅)/2
However , in order to find the exact value of∠ATB we need to evaluate ∅, and to find it , we must have some value of x .
