Question

Urgent geometry

AD is a diameter of E and BE is perpendicular to AD. If m CD = 30°, what is mBEC?

30°
150°
90°
60°

Which of the following combinations cannot be the side lengths of a triangle?

2.3 inches, 3.4 inches, and 3.2 inches
4.8 inches, 5 inches, and 1.2 inches
2.5 inches, 2.5 inches, and 2.5 inches
6.7 inches, 1.1 inches, and 7.9 inches

Answer 1

The best answer is 7 inches 1.1 inches and 7.9 inches

Answer 2

AD and BE is perpendicular => angle BED = 90 deg.

Otherwise angle CED = arc CD = 30 deg

=> angle BEC = angle BED - angle CED = 90 - 30 = 60 deg

Suppose a, b and c are 3 sides of a triangle in which a < b < c.

As property of length of sides a, b, and c of a triangle:

c - b < a < c + b

b - a < c < b + a

c - a < b < c + a

=> 6.7 inches, 1.1 inches, and 7.9 inches are not sides of a triangle

Check:

7.9 - 1.1 < 6.7 <=> 6.8 < 6.7 <=> invalid!

Hope this helps!

:)