TheCATExam
Sign in

CAT 2003 Slot 2 — QA Question 45

Tangents & SecantsEasy
Passage / Data

Answer the following question based on the information given below.

A string of three English letters is formed as per the following rules:

  1. The first letter is any vowel.
  2. The second letter is m, n or p.
  3. If the second letter is m, then the third letter is any vowel which is different from the first letter.
  4. If the second letter is n, then the third letter is e or u.
    1. If the second letter is p, then the third letter is the same as the first letter.

In the figure given below (not drawn to scale), A, B and C are three points on a circle with centre O. The chord BA is extended to a point T such that CT becomes a tangent to the circle at point C. If ∠ATC = 30° and ∠ACT = 50°, then the angle ∠BOA is:

Answer & solution

  • 100°

  • B

    150°

  • C

    80°

  • D

    Cannot be determined

Solution

In ∆ACT,

∵ ∠ACT = 50° and ∠ATC = 30°,

∴ ∠CAT = 100°

Applying the Alternate Segment theorem,

∠ABC = 50°

Since ∠CAT is the external angle of ∆ABC, the sum of ∠ABC and ∠BCA is 100°,

∴ ∠BCA = 50°

∴ ∠BOA = 100°

Hence, option (a).

CAT 2003 Slot 2 QA Q45: In the figure given below (not drawn to scale), A, B and C are three points on a circle with centre O. The cho — Solution | TheCATExam