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Theorem 10.10: If a line segment joining two points subtends equal angles at two other points lying on the same side of the line containing the line segment, the four points lie on a circle (i.e. they are concyclic). Theorem…
Read MoreTheorem 10.11: The sum of either pair of opposite angles of a cyclic quadrilateral is 180 degree. Theorem 10.10 Theorem 10.12 Prerequisite If there exists a circle such that all four vertices of a quadrilateral passes through it, then it…
Read MoreTheorem: Prove that angle in a semicircle is a right angle. OR Prove that angle subtended by a diameter is always a right angle. Theorem 10.8 Theorem 10.10 The proof of this theorem 10.8 is a prerequisite to prove this…
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Theorem 10.9: Angles in the same segment of a circle are equal. Theorem 10.8 Theorem 10.10 Prerequisite The proof of this theorem 10.8 is a prerequisite to prove this theorem. To prove that angles subtended by an arc in the…
Read MoreTheorem 10.8: The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle. Theorem 10.7 Theorem 10.9 This is a very important theorem on circles…
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Question 6: A circular park of radius 20m is situated in a colony. Three boys Ankur, Syed and David are sitting at equal distance on its boundary each having a toy telephone in his hands to talk each other. Find…
Read MoreQuestion 5: Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius 5m drawn in a park. Reshma throws a ball to Salma, Salma to Mandip, Mandip to Reshma. If the distance between…
Read MoreQuestion 4: If a line intersects two concentric circles (circles with the same centre) with centre O at A, B, C and D, prove that AB = CD (see Fig. 10.25). Question 3 Question 5
Read MoreQuestion 3: If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the centre makes equal angles with the chords. Question 2 Question 4
Read MoreQuestion 2: If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord. Question 1 Question 3
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