Question

guys plz help me with this question, no spams!!
the tangent at a point C of a circle and a diameter AB when extended intersect at P. If angle PCA=110° , find angle CBA..​

Answer 1

Answer:

Given

∠PCA = 110°

PC is the tangent to the circle whose centre is O.

Construction

Join points C and O.

∠BCA = 90° [Since angle in a semi circle is 90°]

Also ∠PCO = 90° [Since radius ⊥ tangent]

From the figure we have,

∠PCA =∠PCO + ∠OCA

i.e. 110° = 90° + ∠OCA

Therefore, ∠OCA =20°

Now in ΔAOC, AO = OC [Radii]

So, ∠OCA = ∠OAC =20°

In ΔABC, we have

∠BCA = 90° & ∠CAB = 20°

Therefore,  ∠CBA = 70°