Exams › JEE Main › Maths
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.
- 40 deg
- 70 deg
- 110 deg
- 20 deg
Correct answer: 40 deg
Solution
Inscribed angle AEC = 110 deg subtends the minor arc AC, so the central angle AOC (reflex side) relates as: the arc not containing E has central angle = 2*110 = 220 deg, hence the central angle AOC on E's side = 360 - 220 = 140 deg. In quadrilateral OABC, OA perpendicular to BA and OC perpendicular to BC give angles 90 deg at A and C. Sum of quadrilateral angles = 360: angle ABC = 360 - 90 - 90 - 140 = 40 deg.
Related JEE Main 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.
- 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.
- 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.
- Let A be the set {(n, 2n): n ∈ N} and let B be the set {(2n, 3n): n ∈ N}. What is the intersection A ∩ B?
- Let set A contain 3 elements and set B contain 6 elements. Then the cardinality of their union must satisfy
- Given the sets A = {1, 2, 5} and B = {3, 4, 5, 9}, what is A ∩ B?
⚔️ Practice JEE Main Maths free + battle 1v1 →