## Exam-Style Questions on Geometry## Problems 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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