Geometry: Angles, Circles & Proof

In the diagram, A, B, C, D lie on a circle centre O. TA is tangent to the circle at A. Angle ADC = 118° and angle BAT = 40°. Find, giving a reason for each answer, (a) angle ABC. [2] (b) angle ACB. [2] (c) reflex angle AOC. [2]

In the diagram, angle ACB = angle DAB, AB = 6 cm and BC = 2 cm. (a) Show that △ABC and △DBA are similar. [2] (b) Find the length of CD. [2] (c) Given that the area of △DBA is 36 cm², find the area of △ABC. [2]

Two concentric circles have centre O. PQ is a diameter of the larger circle and RS is a diameter of the smaller circle. PS and RQ are tangents to the smaller circle. The radius of the larger circle is 17 cm and the radius of the smaller circle is 8 cm. (a) Show that △PSO ≅ △QRO, stating your reason clearly. [2] (b) Calculate the area of △QRO. [3]