The seamstress was so impoverished that she was unable to provide for her feverish infant, so the Happy Prince gifted her a ruby. After being convinced by the prince, the swallow proceeded to the seamstress's home. The swallow left the ruby on the table where the woman worked since she had fallen asleep. Then, using his wings, he circled the bed, fanning the boy's forehead. The boy fell asleep as a result of feeling more at ease.
Two circles intersect at two points B and C. Through B, two line segments ABD and PBQ are drawn to intersect the circles at A, D and P, Q respectively (see Fig. 9.27). Prove that ∠ACP = ∠ QCD

ABCD is a trapezium in which AB || CD and AD = BC (see Fig. 8.14). Show that
(i) ∠A = ∠B
(ii) ∠C = ∠D
(iii) ∆ABC ≅ ∠∆BAD
(iv) diagonal AC = diagonal BD [Hint : Extend AB and draw a line through C parallel to DA intersecting AB produced at E.]

(i) The kind of person the doctor is (money, possessions)
(ii) The kind of person he wants to be (appearance, ambition)