Draw OM perpendicular AB and ON perpendicular AC Join OA. In right △OAM, OA2 = OM2 + AM2 ⇒ r2 = p2 + (1/2AB)2 (Since,OM perpendicular AB, ∴ OM bisects AB ) ⇒ 1/4AB2 = r2 - p2 or AB2 = 4r2 - 4p2 ...(i) In right △OAN, OA2 = ON2 + AN2 ⇒ r2 = q2 + (1/2AC)2 (Since ON perpendicular AC, ∴ ON bisects AC ) ⇒ 1/4AC2 = r2 - q2 or 1/4(1/2AB)2 = r2 - q2 (Since AB = 2AC) ⇒ 1/16AB2 = r2 - q2 or AB2 = 16r2 - 16q2 ....(iii) From (i) and (ii), we have 4r2 - 4p2 = 16r2 - 16q2 or r2 - p2 = 4r2 - 4q2 or 4q2 = 3r2 + p2