The inscribed angle on the circumference of the circle subtended by the diameter at the center is a right angle
What can be said about segment AB is; Segment AB is the diameter of circle with midpoint at C
What can be said about angle BDA is; Angle BDA is an inscribed angle of the circle with midpoint at C, subtended by the diameter AB at the center
The measure of angle BDA is 90°
What can be said about angle BEA is; Angle BEA is an inscribed angle of the circle with midpoint at C, subtended by the diameter AB at the center
The measure of angle BEA is 90°
The given diagram shows;
Circle with midpoint <em>C</em>, along AB, and radius AC
The diameter of circle C = AB
Circle with midpoint <em>A</em>, intersecting with circle <em>C</em> at points <em>D</em> and <em>E</em>
Tangents from point B on circle, <em>C</em>, intersect with circle <em>A</em> at points <em>D</em> and <em>E</em>
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Required parameters;
- What can be said about AB
The segment AB is a line that intersects the circle <em>C</em> at two points and also passes through the the point <em>C</em> which is the center of the circle <em>C</em>
Therefore, the segment AB is the diameter of the circle with center at <em>C</em>
- What can be said about angle BDA
The angle BDA is the inscribed angle of circle <em>C</em> subtended by the points <em>A</em> and <em>B</em> which specifies the diameter of the circle with midpoint <em>C</em>
Therefore, the angle BDA is subtended by the diameter of the circle at the center
According to circle theorem, we have;
Angle subtended at the center = 2 × The angle subtended at the circumference
The angle subtended at the center by the diameter AB = 180° (Angle on a straight line)
Therefore;
The angle subtended at the center = 180° = 2 × Angle BDA
Angle BDA = 180°/2 = 90°
Angle BDA = 90°
- What can be said about angle BEA
Similarly, we have;
The angle subtended at the center = 180° = 2 × Angle BEA
Angle BEA = 180°/2 = 90°
Angle BEA = 90°
Find out more about inscribed angles of a circle here:
brainly.com/question/17021375
