Question

AOD is the diameter of a circle with centre O. AB and CD are two equal chords of the circle such that the chords are not intersecting and LBOC=40°. Write the measure of LABO (in degrees)

Answer 1

Answer:

Join AE, OB and OC

:: Chord AB = Chord BC = Chord CD

[given]

.. LAOB = LBOC = LCOD

(Equal chords subtends equal angles at

the centre)

But ZAOB + LBOC + <COD = 180°

[AOD is a straight line]

LAOB = LBOC =LCOD = 60°

In LOAB, OA = OB

..LOAB = LOBA

the same circle]

[radii of

But OAB + OBA = 180° - AOB

= 180° -60°

= 120°

:: ZOAB = ZOBA = 60°

In cyclic quadrilateral DEF,

DEF + ZDAF =180°

ZDAF = 180° - DEF

= 180° -110°

= 70°

Now, 2FAB = <DAF +<OAB = 70° +60° = 130°