Context for question 16A, B, C, D and E lie on a circle, centre O. FG is a tangent to the circle at E. Angle ABE=35∘ and angle CBE=75∘.
16(a)Circle TheoremsEasy2 marksFind the value of x and the value of y.x =y =Grade answerGrading criteria
16(b)Circle TheoremsMedium1 markComplete this statement with the geometrical reason. Obtuse angle EOC=150∘ becauseAAngles in the same segment are equalBAngle in a semicircle is 90∘COpposite angles of a cyclic quadrilateral add up to 180∘DAngle at the centre of a circle is twice the angle at the circumferenceEThe angle between a tangent and a radius is 90∘FAngle between a tangent and a chord is equal to the angle in the alternate segmentGTangents from an external point are equal in lengthHThe perpendicular from the centre to a chord bisects the chordGrade answerSolutionGrading criteria
16(c)Perimeter AreaMedium3 marksThe radius of the circle is 6 cm. Work out the area of the major sector EOC. Give your answer in terms of π in its simplest form.Answercm2Grade answerGrading criteria