Geometry — practice questions, page 5
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A circle of radius 2 cm is inscribed in a right-angled triangle whose hypotenuse is 13 cm. Find…Two circles of radii 10 cm and 6 cm touch each other internally. How far apart are their centres?From a point P outside a circle, the tangent PT is 12 cm long. A line from P through the centre…TA is the tangent at A to a circle, AB is a chord with ∠TAB = 50°, and C is a point on the major…What can be said about the tangents drawn at the two ends of a diameter of a circle?A circle is inscribed in an isosceles trapezium whose parallel sides are 8 cm and 18 cm. What is…PA and PB are tangents from P to a circle with centre O and radius 9 cm. If PA = 12 cm, what is…Two circles, each of radius 5 cm, are drawn so that each passes through the centre of the other.…In triangle ABC, ∠C = 90°, AC = 6 cm and BC = 8 cm. What is the distance between its incentre and…PQ is a tangent at Q to a circle with centre O and radius 10 cm. If OP = 26 cm, what is the area…The diagonals of a rhombus are 16 cm and 30 cm. What is the length of each side?A rectangle has a perimeter of 34 cm and a diagonal of 13 cm. What is its area?Two adjacent angles of a parallelogram are in the ratio 2 : 3. What is the larger angle?A rhombus has sides of 13 cm and one diagonal of 24 cm. What is its area?One angle of a rhombus is 60° and each side is 10 cm. How long is the shorter diagonal?The bisectors of ∠A and ∠B of parallelogram ABCD meet at P. What is ∠APB?ABCD is a parallelogram with AB = 11 cm and AD = 7 cm. The bisector of ∠A meets DC at E. Find EC.The parallel sides of a trapezium are 12 cm and 20 cm. How long is the segment joining the…An isosceles trapezium has parallel sides of 10 cm and 24 cm, and each non-parallel side is 25 cm.…In trapezium ABCD, AB ∥ DC and AB = 3 × DC. The diagonals meet at O. If the area of triangle COD…The diagonals of rectangle ABCD meet at O, and ∠AOB = 64°. Find ∠OAD.The midpoints of the sides of a quadrilateral of area 84 cm² are joined in order. What is the area…A parallelogram has sides 7 cm and 9 cm, and one diagonal is 8 cm. How long is the other diagonal?Each side of a rhombus is 10 cm and its diagonals differ by 4 cm. What is its area?ABCD is a parallelogram and E is the midpoint of BC. AE cuts the diagonal BD at F. If BD = 18 cm,…
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