Question

In the given figure, the tangent at a point C of a circle and a diameter AB when extended intersect at P.
If PCA = 130°, find CBA.

Answer 1

Step-by-step explanation:





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Question



The tangent at a point C of a circle and a diameter AB when extended intersect at P. If ∠PCA=1100 , find ∠CBA .Hint : Join C with centre O.



A,O,B,P all are on the same line and P and C are points on the tangent.

AB is a diameter of a circle.

∴  ∠BCA=90o              [ Angle inscribe in a semi-circle. ]

C is the point on the circle where the tangent touches the circle.

⇒  So, ∠OCP=90o.

⇒  ∠PCA=∠PCO+∠OCA

⇒  110o=90o+∠OCA

⇒  ∠OCA=20o

In △AOC,

⇒ AO=OC             [ Radius of a circle. ]

⇒  ∠OCA=∠CAO=20o

In △ABC,

⇒  ∠CAB+∠CBA+∠BCA=180o

⇒  20o+∠CBA+<

CBA=70°