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  Item Reference: KCLCAL-1881-1882-639

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640 GENERAL LITERATURE AND SCIENCE 23 Find the radii of the inscribed and escribed circles of triangle and show that the square root of their continued product is equal to the area of the triangle 24 In regular hexagon whose side is circle is inscribed and in this circle another regular hexagon and so on until there are in all η hexagons find the sum of the areas of the hexagons XVII eonutrm If two triangles have two sides of the one equal to two sides of the other each to each and have also the angles contained by those sides equal to one another they shall also have their bases or third sides equal and the two triangles shall be equal and their other angles shall be equal each to each namely those to which the equal sides are opposite If side of any triangle be produced the exterior angle is equal to the two interior and opposite angles and the three interior angles of every triangle are together equal to two right angles Construct right-angled triangle having given the hy- potenuse and the perpendicular upon it from the right angle triangle is isosceles when the same line bisects its base and vertical angle In any right-angled triangle the square on the side sub- tending the right angle is equal to the squares on the sides containing the right angle If two exterior angles of triangle are bisected the line joining the point cf intersection of the bisecting lines with the third angle of the triangle bisects that angle In every triangle the square on the side subtending an acute angle is less than the squares on the sides containing that angle by twice the rectangle contained by either of these sides and the straight line intercepted between the perpen- dicular let fall on it from the opposite angle and the acute angle
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