Question

Circles - Class 'X'

Mathematics

Answer 1

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Answer 2

In Δ CAB ,

∠ACB = 90° [ angle in a semi-circle is 90° ]

∠CAB = 30° [ given ]

We know that :

∠CAB + ∠ACB + ∠CBA = 180° [ angle sum property ]

∠CBA + 90° + 30° = 180°

==> ∠CBA = 180° - ( 90° + 30° )

==> ∠CBA = 180° - 120°

==> ∠CBA = 60°

Now :

∠PCA = ∠CBA [ alternate segment ]

==> ∠PCA = 60°

Hence ∠PCA = 60° is the answer .

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