Question

2. The two circles intersect at points C and D. Two straight lines passing through points D and C intersect one circle at points A and B respectively and the other circle at points E and F respectively. If ∠DAB = 75∘∠DAB = 75∘, DEF =?​

Answer 1

Answer:

$\huge{\underline{\mathtt{\red{❥A}\pink{N}\green{S}\blue{W}\purple{E}\orange{R}}}}$Join AB and 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^{\circ}

∠ABD+∠ACD=180 °

Also, ∠ABD=∠ABP=180 °

(Linear Pair)

∴∠ACD=∠ABP ...........(ii)

From (i) and (ii),

∠ACD=∠APX

∴XY∥CD (Since alternate angles are equal).