Geometry — practice questions, page 4
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The line joining (1, 3) and (4, k) is perpendicular to the line 2x − 3y + 7 = 0. What is the value…What are the coordinates of the foot of the perpendicular drawn from the point (4, 1) to the line…A quadrilateral has vertices, taken in order, at (1, 1), (7, −3), (12, 2) and (7, 21). What is its…The point P divides the join of A(1, −2) and B(5, 4) externally in the ratio 3 : 1. What are the…A triangle has vertices at (1, 2), (3, −4) and (5, −6). What are the coordinates of its…A and B are two fixed points in a plane. A point moves so that it is always the same distance from…Two straight lines intersect at a point O. A point moves so that its perpendicular distances from…A rectangular field is 96 m long and its diagonal measures 104 m. What is the width of the field?The three sides of a right-angled triangle are consecutive even numbers of centimetres. What is…Two vertical poles of heights 13 m and 8 m stand on level ground, and their feet are 12 m apart.…In triangle ABC, the point D lies on BC with BD : DC = 1 : 2, and E is the midpoint of AD. The ray…In triangle ABC, the point P lies on AB with AP : PB = 1 : 3, and the point Q lies on AC with AQ :…A triangle has sides 6 cm, 8 cm and 10 cm. What is the sum of the squares of the lengths of its…In triangle ABC, D is the midpoint of AB. A line through D drawn parallel to BC meets AC at E, and…A trapezium is a quadrilateral with at least one pair of parallel sides. In one such trapezium the…ABCD is a quadrilateral inscribed in a circle, with its vertices in order, and the side AB is…Two circles of radii 10 cm and 17 cm intersect, and their common chord is 16 cm long. The two…Two circles share the same centre and have radii 25 cm and 24 cm. A chord of the larger circle…A circle is inscribed in triangle ABC and touches the sides BC, CA and AB at D, E and F…From an external point P, two tangents touch a circle at A and B, and PA = 15 cm. A third tangent…A and B are two fixed points. A point P moves in the plane so that angle APB is always a right…Which point on the y-axis is equidistant from the points (6, 5) and (−4, 3)?A trapezium is defined as a quadrilateral with at least one pair of parallel sides. Using that…In triangle ABC, the point D lies on AB and the point E lies on AC, with DE parallel to BC. If AD…In triangle ABC, AB = AC and the angle at A measures 40°. A point D is taken on side AC so that BD…
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