Geometry — practice questions, page 2
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An exterior angle of a triangle measures 110°. The two remote (opposite) interior angles are in…In triangle ABC, AB = 13, BC = 14 and CA = 15. What is the length of the altitude drawn from A to…From an external point P a tangent PT is drawn to a circle with centre O, touching it at T. If PT…For what value of k are the points A(2, 3), B(4, k) and C(6, −3) collinear?The diagonals of a rhombus measure 16 cm and 30 cm. What is the perimeter of the rhombus?Two triangles are similar. Their areas are 45 cm² and 80 cm². A side of the smaller triangle…In a regular polygon each interior angle exceeds each exterior angle by 132°. How many sides does…In triangle ABC, E is the midpoint of AC and F is the midpoint of AB. The medians BE and CF are…From a point P outside a circle, a secant through P meets the circle first at A and then at B,…What is the area of the triangle whose vertices are (1, 2), (4, 6) and (−3, −2)?A trapezium is defined inclusively as a quadrilateral with at least one pair of parallel sides.…In triangle ABC the angle at A is 90°, and AD is the altitude from A to the hypotenuse BC, with D…A transversal cuts two parallel lines. The bisectors of one pair of co-interior angles (interior…A triangle has sides of length 7, 24 and 25. What is the length of the median drawn to its longest…ABCD is a cyclic quadrilateral in which angle A = (3x − 10)° and angle C = (2x + 20)°. What is the…What are the coordinates of the centroid of the triangle whose vertices are (3, −5), (−7, 4) and…In trapezium ABCD the side AB is parallel to the side DC, with AB = 12 and DC = 20. The diagonals…In triangle ABC, D lies on AB and E lies on AC so that AD : DB = 1 : 2 and AE : EC = 1 : 2. What…In triangle ABC, angle B = 70° and angle C = 50°. The bisectors of angle B and angle C meet at the…In triangle ABC, AB = 8, AC = 12 and BC = 15. The bisector of angle A meets BC at D. What is the…AB is a diameter of a circle and C is a point on the circle, distinct from A and B. If AC = 5 cm…A triangle has vertices at (0, 0), (6, 0) and (0, 8). What are the coordinates of its circumcentre?In quadrilateral ABCD the diagonals AC and BD are perpendicular to each other, with AC = 10 units…The corresponding heights of two similar triangles are in the ratio 3 : 5. If the area of the…Two sides of a triangle measure 8 and 12. How many different integer values are possible for the…
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