9.2 CHAPTER 9. GEOMETRY
ABSˆ +ABTˆ = 90◦(TB⊥ SR)
BATˆ = 90◦(∠s at centre)
∴ABTˆ +ATBˆ = 90◦(sum of angles in�BAT )
∴ABSˆ = ATBˆ
However,AQBˆ = ATBˆ (angles subtended by same chord AB (Theorem 5))
∴AQBˆ = ABSˆ
ABSˆ +ABRˆ = 180◦ (SBR is a straight line)
APBˆ +AQBˆ = 180◦ (APBQ is a cyclic quad. (Theorem 7)
From (9.1), AQBˆ = ABSˆ
∴ 180 ◦−AQBˆ = 180◦−ABSˆ
∴APBˆ = ABRˆ
(9.1)Exercise 9 - 6
Find the values of the unknown letters.