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Example 4: In Fig 10.33, ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If ∠ DBC = 55° and ∠ BAC = 45°, find ∠ BCD. Example 3 Example 5 Prerequisite There are multiple concepts…
Read MoreExample 3: In Fig. 10.32, AB is a diameter of the circle, CD is a chord equal to the radius of the circle. AC and BD when extended intersect at a point E. Prove that ∠ AEB = 60°. Example…
Read MoreExample 2: If two intersecting chords of a circle make equal angles with the diameter passing through their point of intersection, prove that the chords are equal. Example 1 Example 3 Prerequisite Before solving this question, you must be aware…
Read MoreExample 1: Given an arc of a circle, complete the circle. Class 9 | Home Example 2 Prerequisite To complete a circle we need to know its: Center Radius Once we have this information, we can draw the circle. If…
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Theorem 10.12: If the sum of a pair of opposite angles of a quadrilateral is 180 degree, the quadrilateral is cyclic. Theorem 10.11 Class 9 | Home Prerequisite This is relatively bit tricky theorem to prove (not difficult though) in…
Read MoreTheorem 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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