Question

If two sides of a cyclic quadrilateral are parallel ,prove that the remaining two sides are equal and both the diagonal are equal

Answer 1

Answer:

f two opposite sides of a cyclic quadrilateral are parallel then prove that remaining two sides are equal and both the diagonals are equal. Answer: ... Hence, DC = AB i.e. the 2 remaining sides of the cyclic quadrilateral are equal

Step-by-step explanation:

Answer 2

Answer:

Step-by-step explanation:

Let ABCD be the cyclic quadrilateral with AD parallel to BC. The center of the circle is O.

Join AC

Now, since AD is parallel to BC and AC is the transverse

∠DAC=∠ACB (interior opposite angles)

∠DAC is subtended by chord DC on the circumference and ∠ACB is subtended by chord AB.

If the angles subtended by 2 chords on the circumference of the circle are equal, then the lengths of the chords are also equal.

Hence, DC=AB i.e. the 2 remaining sides of the cyclic quadrilateral are equal.

Now, BD and AC are the two diagonals.

In △ABD and △DCA,

AB=CD                    (proved above)

∠DCA=∠DAB       (angles subtended by the same chord AD)

∠ACB=∠DAC       (proved above)

Hence, △ABD is congruent to △DCA (by ASA)

Hence, BD=AC     (by CPCT)