Multiple choice

In a circle with center C and radius 6 2 cm, PQ and SR are two parallel chords separated by one of the diameters. If ∠PQC = 45° and the ratio of the perpendicular distance of PQ and SR from C is 3 : 2, then the area, in sq. cm, of the quadrilateral PQRS is

  1. 20(3 + 14 )

  2. 20( 3 2 + 7 )

  3. 4(3 + 14 )

  4. 4(3 2 + 7 )

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Interpreting the garbled radius as 6sqrt(2) cm, the given angle makes the distance of PQ from the center 6 cm, so the other distance is 4 cm. The chord lengths are 12 cm and 4sqrt(14) cm, giving area ((12 + 4sqrt(14))/2) x 10 = 20(3 + sqrt(14)) sq. cm.