By A.N. Parshin (editor), I.R. Shafarevich (editor), Yu.G. Prokhorov, Yu.G. Prokhorov, S. Tregub, V.A. Iskovskikh

This EMS quantity presents an exposition of the constitution concept of Fano forms, i.e. algebraic forms with an considerable anticanonical divisor. This ebook might be very worthy as a reference and examine consultant for researchers and graduate scholars in algebraic geometry.

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Let us denote the feet of the perpendiculars dropped from the point A on the given lines by M and N, and the feet of the perpendiculars dropped from B by K and L, respectively. Find the angle between the lines MN and KL if LAOB = Ct ~ 90°. 247. Two circles touch each other internally at a point A. A radius OB touching the smaller circle at C is drawn from the centre 0 of the larger circle. Find the angle BAC. 248. Taken inside a square ABCD is a point Msuch thatLMAB = 60°, LMCD = 15°. Find LMBC.

Find the distance between the parallel sides of the triangles ABC and AIBICl • 172. The sides AB and CD of a quadrilateral ABeD are mutually perpendicular; they are the diameters of two equal circles of radius r which touch each other. Find the area of the quadrilateral ABCD if I Be I : I AD I = k. 173. Two circles touching each other are inscribed in an angle whose size is ct. Determine the ratio of the radius of the smaller circle to the radius of a third circle touching both the circles and one of the sides of the angle.

Two circles touching each other are inscribed in an angle whose size is ct. Determine the ratio of the radius of the smaller circle to the radius of a third circle touching both the circles and one of the sides of the angle. 174. In a triangle ABC, circle intersecting the sides AC and BC at points M and N, respectively, is constructed on the Midline DE, parallel to AB, as on the diameter. Find IMN I if IBC I = a, lAC I = b, I AB 1= c. 175. The distance between the centres of two circles is equal to a.