02
Sep
Question 6: ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ∠ DBC = 70°, ∠ BAC is 30°, find ∠ BCD. Further, if AB = BC, find ∠ ECD.
Prerequisite
Most of the questions in this exercise are based on the theorem – same segment angles are equal. We have also used the Isosceles triangle theorem in to solve this question along with the angle sum property of a triangle.
Theorem 10.9: Angles in the same segment of a circle are equal
Theorem 7.2: Angles opposite to equal sides of an isosceles triangle are equal.
Theorem 6.7: The sum of the angles of a triangle is 180º.
Chapter 10 – Circles
