In the diagram, A and B are the centres of two circles that touch at P. The line ACT touches the small circle at T and intersects the large circle at C. D is the point on AB such that CDA = 90°. [Figure showing two touching circles, line ACT, point D on AB]

1. (a)Complete the following, to show that triangle ACD is similar to triangle ABT. In triangle ACD and triangle ABT angle DAC = angle _________ (same angle) angle CDA = angle _________ (.........................................................) angle ACD = angle _________ (two angles in a triangle are equal, so the third angles are equal) Because the three pairs of angles are equal, the triangles are similar.[2]
2. (b)Given that the radii of the circles are 7 cm and 3 cm, calculate CD.[3]

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