The ABCD quadrangle is inscribed in a circle so that the length of the AD side is equal to the radius of the circle

| February 9, 2021 | education

The ABCD quadrangle is inscribed in a circle so that the length of the AD side is equal to the radius of the circle, and the length of the BC side is greater than the radius. It is known that the angle of the internal combustion engine = 50 °, the angle BAD = 115 °. Find the angle in degrees between straight lines AB and CD.

Triangle AOD – Equilateral (AD = Conditional Radius).
The center angle AOD = 60 °, the arc AD on which the center angle AOD rests is 60 °.
The inscribed angle BAD = 115 ° (by condition) rests on the BCD arc, the degree measure of which is twice the angle – 230 °.
The inscribed angle DBC = 50 ° (by condition) rests on the CD arc, the degree measure of which is twice the angle – 100 °.
Arc BC = arc BCD – arc CD = 230 ° – 100 ° = 130 °.
Point H is the intersection point of straight lines AB and CD.
Find the VNS angle – the angle between two secants drawn from one point.
∠ VNS = (arc BC – arc AD) / 2 = (130 ° – 60 °) / 2 = 35 °.
Answer: the angle between lines AB and CD is 35 °.



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