Question

in the figure the tangent at C and diameter AB when extended intersect at P .if angle PCA =110°, find angle CBA​

Answer 1

Answer:

∴ ∠CBA=70 °

Step-by-step explanation:

$Let O be the center of the circle. \\ A,O,B,P all are on the same line and P and C are points on the tangent.</p><p></p><p></p><p> \\ AB is a diameter of a circle. \\ ∴  ∠BCA=90o              [ Angle inscribe in a semi-circle. ] \\ C is the point on the circle where the tangent touches the circle.</p><p></p><p></p><p> \\ ⇒  So, ∠OCP=90o. \\ ⇒  ∠PCA=∠PCO+∠OCA \\ ⇒  110o=90o+∠OCA \\ ⇒  ∠OCA=20o</p><p></p><p></p><p> \\ In △AOC,</p><p></p><p></p><p> \\ ⇒ AO=OC             [ Radius of a circle. ]</p><p></p><p></p><p> \\ ⇒  ∠OCA=∠CAO=20o</p><p></p><p></p><p> \\ In △ABC,</p><p></p><p></p><p> \\ ⇒  ∠CAB+∠CBA+∠BCA=180o</p><p></p><p></p><p> \\ ⇒  20o+∠CBA+90o=180o</p><p></p><p></p><p> \\ ⇒  110o+∠CBA=180o \\ ∴  ∠CBA=70o.</p><p></p><p>$

Answer 2

Step-by-step explanation:

see the tangnet at and the angle PCA is equal to 110° CBAwill be equal to other lengths