...alternate to L ABD and segment Fto LABC. TANGENT PROPEBTIES OF THE OIRCLE Theorem 21. Either angle between a tangent to a circle and a chord drawn from the point of contact is equal to any angle in the alternate segment. X PA Q Given. PAQ touches a circle, of which AB is a chord, at...

...7,9,11 cm. long Fig. 151 206 180. Proposition 15. The angle made by a tangent to a circle with the chord drawn from the point of contact is equal to the angle in the alternate segment of the circle. Let AB be a tangent to the circle (in Fig. 152) at D. Let DE be a chord. Draw a diameter...

...that str. line ; .: they touch each other (Props. 11 and 12). 21 3, 7. Prove that the angle between a tangent to a circle and a chord drawn from the point of contact is half of the angle subtended at the centre by the chord. Let DE touch given QABC, whose centre is O,...