Geometry — practice questions, page 10
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QuestionIn a certain triangle the circumradius measures 10 cm and the inradius measures 3 cm. How far…QuestionA straight line cuts side AB of triangle ABC at F and side CA at E, and meets the line BC at a…QuestionIn triangle ABC the point D lies on the side AB, and the lengths satisfy CD = CB. If ∠ACD = 20°…QuestionIn triangle ABC the angle at A measures 100°. The perpendicular bisector of the side BC cuts the…QuestionThe six interior angles of a convex hexagon are in arithmetic progression, and the smallest of…QuestionWhich point of the plane is equidistant from the three points A(2, 3), B(8, 3) and C(8, 11)?QuestionThe point (5, 2) is reflected in the straight line y = x + 2. What are the coordinates of its image?QuestionA circle has its centre at (3, −4) and the straight line 3x − 4y + 5 = 0 is a tangent to it. What…QuestionG is the centroid of triangle ABC. The line drawn through G parallel to BC meets AB at P and meets…QuestionIn trapezium ABCD the side AB is parallel to the side DC, with AB = 12 cm and DC = 26 cm. P is the…QuestionIn quadrilateral ABCD, named in order, the angle at B and the angle at D are both right angles.…QuestionA student claims to have drawn a regular polygon each of whose interior angles measures exactly…QuestionA convex polygon has exactly twice as many diagonals as it has sides. How many sides does it have?QuestionIdentical copies of one regular polygon are to be fitted edge to edge around a single point,…QuestionTwo circles cut each other at the points A and B. A straight line is drawn through A, meeting the…QuestionThree circles of radii 1 cm, 2 cm and 3 cm are drawn so that each one touches the other two…QuestionIn an acute-angled triangle ABC the angle at A measures 40°. I is the incentre and O is the…QuestionIn triangle ABC the internal bisector of ∠A is produced to meet the circumcircle a second time at…QuestionA triangle has an area of 84 cm² and its three sides add up to 42 cm. What is the radius of its…QuestionA small circle touches a large circle internally. The large circle has radius 15 cm and the two…QuestionIn a circle of radius 17 cm two parallel chords measure 16 cm and 30 cm, and the centre of the…QuestionEach side of a convex pentagon is produced at both ends until it meets the productions of the two…QuestionIn triangle ABC the median AD is drawn to the side BC, and G is the centroid. The line through G…QuestionIn rhombus ABCD the diagonal AC turns out to have exactly the same length as the side AB. What is…QuestionA and B are two fixed points with AB = 6 cm. A point P moves in the plane so that its distance…
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