Further Mathematics: Geometry Topical Past Paper Questions

In the triangle ABC, AB = 8, BC = 12 and AC = 10. A circle is inscribed in this triangle. (a) Find the lengths of the tangents from A, B and C to this inscribed circle. (b) (i) Show that the area of the triangle ABC is $ 15r $, where r denotes the radius of the inscribed circle.…

[Maximum mark: 16] The triangle T is isosceles with AB = AC = d and $ \widehat{BAC} = 2\theta $. In parts (a) and (b) you are required to draw a diagram to illustrate the situation. (a) Find an expression for the radius R of the circumscribed circle of T in terms of d and $ \thet…

[Maximum mark: 24] (a) (i) In a triangle ABC, prove $ \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} $. (ii) Prove that the area of the triangle ABC is $ \frac{1}{2}ab\sin C $. (iii) Given that R denotes the radius of the circumscribed circle prove that $ \frac{a}{\sin A}…