Geometry — practice questions, page 9
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QuestionThe four vertices of quadrilateral ABCD, named in order, lie on one circle. The sides AD and BC…QuestionTwo circles have radii 14 cm and 6 cm, and their centres are 17 cm apart. What is the length of a…QuestionA regular pentagon ABCDE is inscribed in a circle, its vertices named in order round the circle.…QuestionA regular polygon is drawn around a circle so that every one of its sides touches the circle. P…QuestionIn triangle ABC the point D is the midpoint of AB and the point E is the midpoint of AC. F is the…QuestionIn quadrilateral ABCD the diagonals AC and BD meet at O. Which one of these conditions, taken on…QuestionIn quadrilateral PQRS the diagonals PR and QS bisect each other and are equal in length. Which…QuestionA and B are two points lying on the same side of a straight line ℓ. A point X is to be chosen on ℓ…QuestionA and B lie on the same side of a straight line ℓ, at perpendicular distances 3 cm and 5 cm from…QuestionThe four corners of a quadrilateral PQRS, taken in that order, all lie on one circle. The angles…QuestionPT is a tangent drawn from an external point P, touching a circle at T. A secant through P meets…QuestionP, Q, R and S are the midpoints of the sides AB, BC, CD and DA of a quadrilateral ABCD, and PQRS…QuestionIn quadrilateral ABCD the point P is the midpoint of the side AB and the point Q is the midpoint…QuestionTwo circles of unequal radii are drawn apart from each other. A point X is taken outside both of…QuestionTwo circles touch each other externally at the point C. A direct common tangent touches the first…QuestionIn an acute-angled triangle ABC the feet of the three altitudes are joined to form a smaller…QuestionIn quadrilateral ABCD the points B and C lie on the same side of the line AD, and measurement…QuestionTwo circles touch each other internally at the point A, the smaller one lying inside the larger. A…QuestionFour points A, B, C and D lie on a circle in that order, and they cut the circle into four arcs…QuestionThe four vertices of quadrilateral ABCD, named in order, lie on one circle, and the sides measure…QuestionA square and an equilateral triangle are both inscribed in the same circle, and they share the…QuestionTriangle ABC is inscribed in a circle. The arc BC not containing A, the arc CA not containing B…QuestionFrom a point P in the plane of triangle ABC, perpendiculars are dropped to all three sides, each…QuestionH is the orthocentre of an acute-angled triangle ABC. H is reflected in the line BC, and the image…QuestionO is the circumcentre and H the orthocentre of triangle ABC. The circumradius is 10 cm and the…
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