Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | Oct-Nov | (P1-9709/13) | Q#4
In the diagram, D lies on the side AB of triangle ABC and CD is an arc of a circle with centre A and radius 2 cm. The line BC is of length 2√3 cm and is perpendicular to AC. Find the area of the shaded region BDC, giving your answer in terms of and .
It is evident from the diagram that;
First we find the area of the triangle ABC.
Expression for the area of the triangle is;
For the given case;
Now we find area of circular sector ADC.
Expression for area of a circular sector with radius and angle rad is;
We are given that radius of this circular section is 2.
We need to find the area of circular sector ACD.
We know that is a right angled triangle with .
Expression for trigonometric ratio in right-triangle is;
For we take and therefore;
Hence, area of circular sector ACD;
Finally, we can find area of shaded region;