Exams › JEE Advanced › Maths

In a circle, the chord ED is parallel to the diameter AC, and angle CBE = 50 degrees (B is a point on the circle). Find angle CED.

1. 40 degrees
2. 50 degrees
3. 30 degrees
4. 60 degrees

Correct answer: 40 degrees

Solution

Angle CBE and angle CAE subtend the same arc CE, so angle CAE = angle CBE = 50 degrees. Since AC is a diameter, the angle in the semicircle angle AEC = 90 degrees. In triangle AEC, angle ACE = 180 - 90 - 50 = 40 degrees. Because ED is parallel to AC, the alternate angle gives angle CED = angle ACE =... actually angle DEC = angle ECA (alternate angles with transversal EC) = 40 degrees. Hence angle CED = 40 degrees.

Related JEE Advanced Maths questions

• A triangle ABC is inscribed in a circle with centre O, and the angle at A is 60 degrees. From O a perpendicular OD is dropped onto the chord BC. Find the measure of angle BOD.
• From an external point B, two lines BA and BC are drawn tangent to a circle, touching it at A and C respectively. E is a point on the major arc AC such that the inscribed angle AEC = 110 deg. Find the angle ABC.
• Two chords TY and OP of a circle intersect at point K such that TK = 2, KY = 16, and KP = 2*(KO). Find the length OP.
• In a chemistry class, there are 20 students, while a physics class has 30 students. If 10 students are enrolled in both classes, and the two classes are held at separate times, determine the value of k/8, where k represents the total number of students attending either class.
• Given that A represents the divisors of 15, B contains prime numbers less than 10, and C includes even numbers less than 9, how many elements are there in the intersection of (A ∪ C) and B?
• Identify the periodic function among the following:

⚔️ Practice JEE Advanced Maths free + battle 1v1 →