Paper 1 October/November 2005 MATHEMATICH (9709/1) A Levels
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The diagram shows a circle ${C_1}$ touching a circle ${C_2}$ at a point $X$. Circle ${C_1}$ has centre $A$ and radius $6{\text{ }}cm$, and circle ${C_2}$ has centre $B$ and radius $10{\text{ }}cm$. Points $D$ and $E$ lie on ${C_1}$ and ${C_2}$ respectively and $DE$ is parallel to $AB$. Angle $DAX = \frac{1}{3}\pi $ radians and angle $EBX = \theta $ radians.
a) By considering the perpendicular distances of $D$ and $E$ from $AB$, show that the exact value of $\theta $…