Question

In the given figure two circles intersect at two points A and B xy is the tangent at the point P prove that CD is parallel to tangent x y

Answer 1

Step-by-step explanation:

Given: Two circles intersect at A and B.

To prove: CD || tangent at P.Proof: Join AB. Let XY be the tangent at P. Then by alternate segment theorem, ∠ APX = ∠ ABP ……………(i)Next, ABCD is a cyclic quadrilateral, therefore, by the theorem sum of the opposite angles of a quadrilateral is 180°∠ ABD + ∠ ACD = 180°Also ∠ ABD = ∠ ABP = 180° (Linear Pair)

∴ ∠ ACD = ∠ ABP ...........(ii)