M CUBE: Math-e-Matics by Maheshwari Basic Mathematics

Let A be one of the two points of intersection of two circles with centers X and Y. The tangents at A to these two circles meet the circles again at B,C. Let the point P be located so that PXAY is a parallelogram. Show that P is the circumcentre of triangle ABC.

Solution: Since PXAY is a parallelogram, we have PX∥AY. As AY⊥AB, it follows that PX⊥AB. Since AB is a chord of the circle with center X, we conclude that PX is in fact the perpendicular bisector of AB. Similarly, PY is perpendicular bisector of AC. Thus the perpendicular bisectors of two sides, AB and AC, … Continue reading Let A be one of the two points of intersection of two circles with centers X and Y. The tangents at A to these two circles meet the circles again at B,C. Let the point P be located so that PXAY is a parallelogram. Show that P is the circumcentre of triangle ABC.

M CUBE: Math-e-Matics by Maheshwari ARITHMETIC PROGRESSION

ARITHMETIC PROGRESSION – FORMULAS

Arithmetic Progression definition Arithmetic Progression (also called arithmetic sequence), is a sequence of numbers such that the difference between any two consecutive terms is constant. Each term therefore in an arithmetic progression will increase or decrease at a constant value called the common difference, d. Examples of arithmetic progression are: 2, 5, 8, 11,... common difference … Continue reading ARITHMETIC PROGRESSION – FORMULAS