Geometry — practice questions, page 5
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A right-angled triangle has two equal legs and its hypotenuse measures 10 cm. What is the area of…In a circle of radius 25 cm, one chord lies 7 cm from the centre and a second chord lies 20 cm…The points (−1, 3), (2, p) and (5, −5) lie on one straight line. Using the fact that the triangle…A triangle has an obtuse angle at one of its vertices. Of the four classical centres — incentre,…A vertical pole 6 m tall casts a shadow 4 m long on level ground. At the same time of day a tower…Two chords AB and CD of a circle cross at a point P inside the circle. If AP = 6 cm, PB = 4 cm and…ABCD is a rectangle whose diagonals AC and BD meet at O. If angle AOB = 110°, what is the measure…In triangle ABC the angle at B is 90° and the angle at C is 30°. If AB = 9 cm, what is the length…ABCD is a cyclic quadrilateral, with its vertices named in order around the circle, and the side…What is the distance of the point (−9, 40) from the origin?In triangle ABC, AB = AC. A point D is taken on side BC so that AD = BD. If angle BAD = 25°, what…A straight line touches a circle at the point A, and AB is a chord of the circle. The angle…A quadrilateral has vertices, taken in order, at A(−2, −1), B(1, 0), C(4, 3) and D(1, 2). Which…The three interior angles of a triangle are in the ratio 2 : 3 : 4. What is the largest of its…A flat mirror lies on level ground between a boy and a tower. The boy, whose eyes are 1.6 m above…Two parallel chords of a circle of radius 13 cm measure 10 cm and 24 cm, and both lie on the same…ABCD is a rhombus of side 10 cm in which angle ABC = 120°. What is the length of the diagonal AC?D is a point lying inside triangle ABC. The angle BAC measures 50°, angle ABD measures 20° and…From a point P outside a circle two secants are drawn. The first meets the circle at A and then at…Two of the vertices of a triangle are (1, 4) and (5, −2), and the centroid of the triangle is at…The altitude of an equilateral triangle measures 6√3 cm. What is the perimeter of the triangle?In triangle ABC, the point D lies on side AB and the point E lies on side AC. The measurements are…The point (−3, 8) is reflected in the vertical line x = 2. What are the coordinates of its image?Which property is true for the diagonals of every rhombus but is NOT true, in general, for the…A chord PQ of a circle is 16 cm long. A diameter AB of the same circle crosses PQ at the midpoint…
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