In circle E, and are diameters. Angle BCA measures 53°.
Circle E is shown. Line segments A C and B D are diameters. Lines are drawn to connect points B and C and points A and D. Angle B C A is 53 degrees.
What is the measure of arc AD?
53°
74°
106°
180°
Answers
Hi there,
The figure for the question is missing and also seeing the options I think we are required to find the measure of the angle subtended by the arc AD. So, I have attached the figure below which satisfies the question above and have solved it accordingly.Thanks
Answer: Option (2): 74°
Step-by-step explanation:
Given data:
AC & BD are diameters of the circle with centre E.
Angle BCA = 53°
To find: the measure of the angle subtended by the arc AD
Solution:
Join the points B & C and A & D.
Step 1:
∵ BE = CE ….. [radius of the circle]
∴ ∠BCA = ∠CBE = 53° …. [angles opposite to equal sides are also equal]
In ∆ BCE, by using the angle sum property,
∠BEC + ∠BCE + ∠CBE = 180°
⇒ ∠BEC = 180° - (53° + 53°) = 74°
Step 2:
We can see from the figure that, AD subtends ∠AED at the centre.
Thus,
The measure of the angle subtended by arc AD = ∠AED = ∠BEC = 74°
Answer:
B.) 74
Step-by-step explanation: