Geometry — practice questions, page 7
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QuestionIn parallelogram ABCD the sides are AB = 7 cm and BC = 9 cm, and the diagonal AC measures 8 cm.…QuestionP is a point inside an equilateral triangle whose altitude measures 15 cm. The perpendicular…QuestionFrom a point P outside a circle of radius 5 cm two tangents are drawn, touching the circle at A…QuestionHow many triangles ABC, no two of them congruent, can be drawn with AB = 7 cm, BC = 5 cm and ∠A =…QuestionIn trapezium ABCD the side AB is parallel to the side DC, with AB = 9 cm and DC = 15 cm. E is the…QuestionO is the circumcentre of triangle ABC and ∠BAC = 55°. What is the measure of ∠OBC?QuestionWhich one of these pairs of triangles need NOT be similar?QuestionIn a circle of radius 10 cm the chord AB is 12 cm long and lies 8 cm from the centre. A second…QuestionThe ray OC stands on the straight line AOB so that ∠AOC = 4x and ∠BOC = 5x. The ray OD bisects…QuestionP is a point inside rectangle ABCD, whose vertices are named in order. The distances are PA = 2…QuestionA triangle has sides of length 9 cm, 12 cm and 16 cm. Which description of it is correct?QuestionABC is an equilateral triangle inscribed in a circle, and P is a point on the minor arc BC. If PB…QuestionThe three medians of triangle ABC meet at G, and the area of triangle ABC is 48 cm². What is the…QuestionAt each vertex of a triangle one exterior angle is drawn. These three exterior angles are in the…QuestionABCD is a cyclic quadrilateral, its vertices named in order round the circle, in which AB = AD. If…QuestionThe diagonals of a quadrilateral bisect each other at right angles, but the two diagonals have…QuestionIn triangle ABC, AB = 9 cm, AC = 6 cm and BC = 5 cm. The bisector of the exterior angle at A meets…QuestionIn quadrilateral ABCD the diagonals AC and BD cross at P, and the four pieces measure PA = 6 cm,…QuestionIn trapezium ABCD the side AB is parallel to the side DC, and the diagonals AC and BD meet at O.…QuestionIn triangle ABC the angle at B is 75° and the angle at C is 35°. From A both the altitude AD and…QuestionTwo similar triangles have corresponding medians in the ratio 5 : 3. The perimeter of the larger…QuestionThe interior angles of a convex polygon add up to three times the total of its exterior angles,…QuestionIn triangle ABC, AB = AC. The point D lies on AB and the point E lies on AC with AD = AE, and the…QuestionIn a right-angled triangle the hypotenuse is 2 cm longer than the longer leg, and the shorter leg…QuestionIn triangle ABC the point D is the midpoint of BC and the point E is the midpoint of AD. What is…
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