Geometry — practice questions, page 8
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QuestionThe circumcentre of triangle ABC turns out to lie on the side BC itself. What can be concluded…QuestionThe area of parallelogram ABCD is 96 cm². The point P is chosen anywhere on the side DC. What is…QuestionIn triangle ABC the angle at A measures 80°. The bisectors of the exterior angles at B and at C…QuestionIn trapezium ABCD the side AB is parallel to the side DC and the diagonals meet at O. The area of…QuestionThe points A, C, B and D lie on a circle in that order, and the chords AB and CD cross at a point…QuestionP is a point lying outside a circle. One line through P cuts the circle at A and then at B; a…QuestionA tangent drawn from the external point P touches a circle at T. A second line through P cuts the…QuestionTwo tangents drawn from an external point P touch a circle at A and at B. The minor arc AB…QuestionP is a point inside a circle of radius 13 cm, and P is 5 cm from the centre. A chord drawn through…QuestionA circle has centre O and radius 9 cm, and the point P satisfies OP = 21 cm. A line through P…QuestionEvery triangle has a nine-point circle. Which nine points does it pass through?QuestionThe circumradius of a triangle measures 18 cm. What is the radius of its nine-point circle?QuestionIn any triangle the circumcentre O, the centroid G and the orthocentre H lie on one straight line,…QuestionThe midpoints of the three sides of triangle ABC are joined to form the medial triangle. Which one…QuestionIn triangle ABC, AB = 8 cm and AC = 14 cm. D is the midpoint of BC and the median AD measures 9…QuestionIn triangle ABC the internal bisector of ∠A meets BC at D. The measurements are AB = 12 cm, AC =…QuestionIn a triangle, which one of these triples of lines need NOT pass through a single common point?QuestionIn triangle ABC the point D lies on BC with BD : DC = 3 : 2, and the point E lies on CA with CE :…QuestionIn triangle ABC the internal bisector of ∠A is drawn together with the bisectors of the exterior…QuestionA quadrilateral ABCD has all four of its vertices on one circle, named in order round it. The…QuestionA quadrilateral is called cyclic when a single circle can be drawn through all four of its…QuestionAB and CD are two chords of a circle with centre O, and the two chords are equal in length. AB is…QuestionIn a circle of radius 10 cm one chord measures 16 cm and another measures 12 cm. Which chord lies…QuestionOne circle of radius 4 cm lies inside a circle of radius 10 cm, and the two circles touch at…QuestionTwo circles of radii 12 cm and 5 cm lie wholly outside each other, and the length of their direct…
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