Question

AE is the diameter of a circle with centre O,the points B,C,E are on the circle such that AB=BC=CD=DE ,calculate angle DAE

Answer 1

Given:  AE is the diameter, AB=BC=CD=DE

To find:  angle DAE = ?

Solution:

• As we have given that AE id diameter so considering any triangle with the base AE will have one angle as 90°.
• eg: consider triangle DAE, we have ang ADE = 90°.
• Now, since AB=BC=CD=DE is given in the question, so the angle subtended by these sides will be equal.
• Hence ang AOB = ang BOC = ang COD = ang DOE
• So, ang AOB + ang BOC + ang COD + ang DOE = 180°

             (linear pair)

            4( ang AOB) = 180°

            ang AOB = 180° /4 = 45°

• Similarly:

            ang DOE = 45°

• Now, ang ODE = ang OED ............as radius is equal(OD = OE)

• So, ang ODE = ang OED = 67.5° = ang DEA

            ang DEA = 67.5°                               (answer as per question in figure)

• Now, in triangle ADE,

             ang AED + ang EDA + ang DAE = 180°

            67.5° + 90° + ang DAE = 180°

            ang DAE = 180° - (67.5° + 90°)

             ang DAE = 22.5°       (answer as per question in the question typed)

Answer:

              So the angle DEA is 67.5°.