![]() ![]() O is the centre of the circle and AB is a chord. Angles In an isosceles trapezoid, the base angles have the same measure pairwise. PQ and RS are two mutually prependicular chords of a circle. The diagonals divide each other into segments with lengths that are pairwise equal in terms of the picture below, AE DE, BE CE (and AE CE if one wishes to exclude rectangles). Write the relation between PA, PB, PC, PD If AB = 5, BP = 3, P D = 2 then find CD? Draw the figure. In the figure AB, C Dare extended and intersect at P. Prove that ABCD given in the figure is cyclic (∵ PQ || BC, QC is the bisector, so the sum of alternate angles are 180°)įrom (1) and (2) we conclude that BPQC is an cyclic trapezium (The line joining midpoints of two sides of a circle will be parallel to the third side). P is the midpoint of AB and Q is the midpoint of AC. (Sum of the alternate angles of a cyclic quadrilateral is 180″) ![]() ∠A + ∠C = 180° (Sum of the opposite angles of a cyclic quadrilateral is 180°) If the vertices are on a circle, prove that it is an isosceles trapezium draw figure Y + 5y = 180 (Sum of the opposite angles of a cyclic quadrilateral is 180°) If we draw a circle taking BC as diameter, ∠A 4x = 180° => 4x = 45° If we draw a circle taken in a AC as diameter, ∠B = 90°, Therefore the point B on the circle. What is the position of the point C based on the circle with diameter AB?ĪB2 + BC2 = 82 + 62 = 64 + 36 = 100 = AC2 What is the position of A based on the circle with BC as the diameter? Why?Ĥ. What is the position of B based on the circle with AC as the diameter? Why?ģ. In triangle ABC, AB = 8cm, BC = 6cm, AC = 10cm.Ģ. PB = 8 cm, PC = 5 cm Circles Orukkam Questions & Answers Taking BC as diameter and drawing a circle, ∠A ( PC If circles are drawn with each side of a triangle of sides 5 centimetres, 12 centimetres and 13 centimetres, as diametres, then with respect to each circle, where would be the third vertex? ∠B = 55° (90 > 55°)ĭrawing diagonal BD and taking it as diameter of a circle.Īs both angles are greater than 90, they lie inside the circle. ∴ The top comer will be outside the circleįor each diagonal of the quadrilateral shown, check whether the other two corners are inside, on or outside the circle with that diagonal as diameterĭrawing diagonal AC and taking it as diameter of a circle As, ∠D = 90°ĭ will be on the circle. Find out whether the top corner of each triangle is inside the circle, on the circle or outside the circle.Īs 110° > 90° the top comer will be inside the circle Suppose we draw a circle with the bottom side of the triangles in the picture as diameter. any quadrilateral with at least one axis of symmetry through a pair of opposite. Some sources would qualify all this with the exception: excluding rectangles. Kerala State Syllabus 10th Standard Maths Solutions Chapter 2 Circles Circles Text Book Questions and Answers An isosceles trapezoid (isosceles trapezium in British English) is a quadrilateral with a line of symmetry bisecting one pair of opposite sides, making it automatically a trapezoid. You can Download Circles Questions and Answers, Activity, Notes, Kerala Syllabus 10th Standard Maths Solutions Chapter 2 help you to revise complete Syllabus and score more marks in your examinations. ![]()
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