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Exam-Style Questions on GeometryProblems on Geometry adapted from questions set in previous Mathematics exams. |
1. | GCSE Higher |
The diagram shows a circle with its centre at the origin.
The red line AB is a tangent to the circle at the point B.
Angle OAB is 30°.
Point A has coordinates \((-10, 0)\)
Point C has coordinates \((5c, -2c)\)
Find the value of \(c\) giving your answer correct to three significant figures and showing all of your working.
2. | IB Studies |
The vertices of quadrilateral ABCD are A (2, 4), B (-1, 5), C (–3, 4) and D (–2, 2).
(a) Calculate the gradient of line CD.
(b) Show that line AD is perpendicular to line CD.
(c) Find the equation of line CD. Give your answer in the form \(ax+by=c\) where \(a,b,c\in \mathbf Z\)
Lines AB and CD intersect at point E.
(d) Find the coordinates of E.
(e) Find the distance between A and D.
The distance between D and E is \(\sqrt{20}\).
(f) Find the area of triangle ADE.
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