Question

In a circle with centre o ab is a diameter and cd is a chord such that abcd is a trapezium bac 40 cad

Answer 1

∠CAD = 10°  if In a circle with centre o ab is a diameter and cd is a chord such that abcd is a trapezium & ∠BAC = 40°

Step-by-step explanation:

∠BAC = 40°

∠ACB = 90° ( angle in semicircle)

ABCD is a trapezium

so CD || AB

=> ∠ACD = ∠BAC  ( alternate angle)

=> ∠ACD =  40°

∠BCD = ∠ACB + ∠ACD

=> ∠BCD =  90° + 40°

=> ∠BCD =  130°

ABCD is cyclic Quadrilateral as all point lies on same circle

=> ∠BAD + ∠BCD = 180°

=>  ∠BAD + 130° = 180°

=> ∠BAD = 50°

∠BAD  = ∠BAC + ∠CAD

=> 50° = 40° + ∠CAD

=> ∠CAD = 10°

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AB is the diameter of a circle with Centre O

Abcd is a cyclic quadrilateral

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