theorems on circles

Example 6: Prove that the quadrilateral formed (if possible) by the internal angle bisectors of any quadrilateral is cyclic. Example 5 Class 9 | Home Prerequisite It is quite an interesting question to solve. The proof explained in this video…

Example 5: Two circles intersect at two points A and B. AD and AC are diameters to the two circles (see Fig.10.34). Prove that B lies on the line segment DC. Example 4 Example 6 Prerequisite If we prove that…

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…

Example 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…

Example 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…

Example 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…

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…

Theorem 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…