SSC CGL Model Paper 1

Question : 52 of 100

Marks: +1, -0

In the given figure, a tangent TA touches the circle with centre 'O' at A. AC is a chord of the circle. ∠ABC =115°. Then find ∠CAT?

Solution:

∠ABC + ∠ADC = 180°

(opposite angles of cyclic quadrilateral)

∠ADC = 180° - 115° = 65°

∠AOC = 2∠CDA

[0 being circumcentre of

∆ADC

]

∠AOC = 2×65 = 130°

Now, OA = OC [radii of the given circle]
So,

∠OAC =∠OCA

∆OAC; ∠OAC +∠OCA + ∠AOC = 180°

2∠OAC = 180° - 130°

∠OAC = 25°

Also, OA is

⊥^τ

to TA
So,

∠CAT = ∠ZOAT - ∠OAC

= 90° - 25° = 65°

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