Aug 22, 2018 · If the side BC of ΔABC is produced to D, then ∠AÇD is called an exterior angle of ΔABC at C, while ∠BAC and ∠ABC are called its interior opposite angles. It is denoted by exterior ∠ACD. A quadrilateral ABCD is called a cyclic quadrilateral, if all the four vertices A B, C and D are concyclic, i.e. A, B, C and D lie on a circle. In Fig. 25.4, ABCD is a cyclic quadrilateral. The sum of opposite angles of a cyclic quadrilateral is always 80°, i.e. they are supplementary. Procedure

The exterior angle of a cyclic quadrilateral is equal to the interior opposite angle. A radius or diameter that is perpendicular to a chord divides the chord into two equal parts and vice versa. A tangent to a circle is perpendicular to the radius drawn to the point of tangency.
Oct 23, 2014 · Proving that the exterior angle of a cyclic quadrilateral is equal to the opposite interior angle We need to show that for the angles of the cyclic quadrilateral, C + E = 180° = B + D (see fig 1) ('Cyclic quadrilateral' just means that all four vertices are on the circumference of a circle.) If you've looked at the proofs of the previous theorems, you'll expect the first step is to draw in radiuses from points on the circumference to the ...

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If the bisectors of the opposite angles of a cyclic quadrilateral ABCD intersect the circle circumscribing it at the points P and Q, prove that PQ is a diameter of ...

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