Geometry — practice questions, page 6
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A lamp is fixed at the top of a post 6 m high. A man 1.8 m tall walks away from the foot of the…The diagonal of a square measures 18 cm. What is the area of the square?In triangle ABC the angle at B is 80° and the angle at C is 40°. The bisector of angle A meets BC…Which one of the following sets of three points is collinear?In triangle ABC the angle at B is a right angle, AB = 20 cm and BC = 21 cm. What is the area of…A tangent touches a circle with centre O at the point T, and P is a point on that tangent. TA is a…In triangle ABC the point D lies on side AC, and angle ABD is equal to angle ACB. If AB = 6 cm and…A quadrilateral has vertices, taken in order, at P(3, 0), Q(4, 5), R(−1, 4) and S(−2, −1). Which…In triangle ABC, AB = AC and the angle at A measures 40°. The side BC is produced beyond C to a…Two vertical poles, 6 m and 12 m high, stand on level ground some distance apart. A wire runs from…From an external point P a secant meets a circle first at C and then at D, with PC = 3 cm and CD =…A rectangle has a perimeter of 46 cm and a diagonal of 17 cm. What is its area?A trapezium is a quadrilateral with at least one pair of parallel sides. A quadrilateral has…Where is the orthocentre of a right-angled triangle located?In triangles ABC and PQR it is given that AB = PQ, ∠A = ∠P and ∠C = ∠R. Which criterion…A, B, C and D lie on a circle in that order, and the chords AC and BD cross at the point P inside…In a quadrilateral ABCD the diagonals AC and BD measure 18 cm and 24 cm. The points P, Q, R and S…In triangle ABC the three medians meet at G, and D is the midpoint of BC. If GD = 4 cm and the…In triangle ABC the point D lies on side AB and the point E lies on side AC. For which one of…A regular pentagon and a regular hexagon are drawn on a flat surface so that they share one…In quadrilateral PQRS the sides satisfy PQ = PS and RQ = RS, and both diagonals PR and QS are…H is the orthocentre of an acute-angled triangle ABC in which ∠BAC = 70°. What is the measure of…The tangent drawn to a circle at the point A is parallel to the chord BC of the same circle. Which…In triangle ABC the bisector of ∠A meets BC at D, and measurement gives BD = 4.5 cm and DC = 6 cm.…Two parallel lines ℓ and m run across the page with ℓ above m, and the point P lies in the strip…
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