Question

in the figure PR and QS are two diameters is PQ equal to Rs

Answer 1

Hey user!!

ACCORDING TO CYCLIC QUADRILATERAL,, if the diagonals of a cyclic quad. is equal then the opp. sides of it must be equal..
THIS STATES BY A THEOREM.

SO, WHEN THE DIAGONALS ARE EQUAL THEN YOU CAN SAY THAT OPP. SIDES ARE EQUAL ..THAT IS PQ=RS..

HOPE IT HELPS U
THANKS..

Answer 2

Given that PR and QS are diameters.
Therefore, OP=OR=OQ=OS (radius of the circle ) 
In triangle POQ and triangle SOR, 
OP=OR (radius ) 
OQ=OS (radius) 
angle POQ = angle SOR (vertically opposite angles ) 
Therefore triangle POQ congruent to triangle SOR (by SAS congruence criteria )
That is , PQ = SR (CPCT )