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Previous Year Paper

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CAT-2003-Previous Years Paper

Question
28 out of 50
 

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



A 100°

B 150°

C 80°

D Not possible to determine

Ans. A

BAC = ACT + ATC = 50 + 30 = 80°

And ACT = ABC (Angle in alternate segment)

So ABC = 50°

BCA = 1870 – (ABC + BAC)= 180 – (50 + 80) = 50°

Since BOA = 2BCA = 2 × 50 = 100°

Alternative Method:

Join OC

OCT = 90° (TC is tangent to OC)

OCA = 90° – 50° = 40°

OAC = 40° (OA = OC being the radius)

BAC = 50° + 30° = 80°

OAB = 80° – 40° = 40° = OBA (OA = OB being the radius)

BOA = 180° – (OBA + OAB) =100°

CAT-2003-Previous Years Paper Flashcard List

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