Apollonius Theorem | Class X (Important Theorem and its application)

#45 CBSE | 2 Marks | Find the ratio in which y-axis divides the line segment joining the points A(5, – 6) and B(– 1, – 4). Also find the coordinates of the point of division. | Class X | IMP Question

#47 CBSE | 2 Marks | The x-coordinate of a point P is twice its y-coordinate. If P is equidistant from Q(2, – 5) and R(– 3, 6), find the coordinates of P | Class X | IMPORTANT

#49 CBSE | 2 Marks | In given fig., AP and BP are tangents to a circle with centre O, such that AP = 5 cm and angle APB = 60°. Find the length of chord AB. | Class X | IMPORTANT

#44 CBSE | 2 Marks |If x = / and x = – 3 are roots of the quadratic equation ax2 + 7x + b = 0, find the values of a and b. | Class X | IMP Question

#48 CBSE | 2 Marks | How many terms of the A.P. 18, 16, 14,……. be taken so that their sum is zero? | Class X | IMPORTANT

#43 CBSE | 2 Marks | Solve for x :√(+) - (2x – 7) = 0 | Class X | IMP Question

#42 CBSE | 2 Marks | Solve for x : √(+) + x = 13 | Class X | IMP Question

#41 CBSE | 2 Marks | In Fig., from an external point P, two tangents PT and PS are drawn to a circle with centre O and radius r. If OP = 2r, | Class X | IMP Question

#40 CBSE | 2 Marks | The 4th term of an A.P. is zero. Prove that the 25th term of the A.P. is three times its 11th term. | Class X | IMP Question

#39 CBSE | 2 Marks | Prove that the points (3, 0), (6, 4) and (– 1, 3) are the vertices of a right angled isosceles triangle. | Class X | IMP Question

#38 CBSE | 2 Marks | In Fig., a quadrilateral ABCD is drawn to circumscribe a circle, with centre O, in such a way that the sides AB, BC, CD and DA touch the circle at the points P, Q, R and S respectively. Prove that: AB+ CD = BC + DA. | Class X | IMP Q

#37 CBSE | 2 Marks | Let P and Q be the points of trisection of the line segment joining the points A(2, – 2) and B(– 7, 4) such that P is nearer to A. Find the coordinates of P and Q. | Class X | IMP Question

#36 CBSE | 2 Marks | If – 5 is a root of the quadratic equation 2x2 + px – 15 = 0 and the quadratic equation p(x2 + x) + k = 0 has equal roots, find the value of k. | Class X | IMP Question

#35 CBSE | 2 Marks | Given below is a cumulative frequency distribution table. Corresponding to it, make an ordinary frequency distribution table. | Class X | IMP Question

#34 CBSE | 2 Marks | Prove the following identity : [ ( −)/( −) ]2 = tan2A : angle A is acute | Class X | IMP Question

#33 CBSE | 2 Marks | In an isosceles triangle ABC right angled at B, prove that AC^2 = 2AB^2 | Class X | IMP Question

#32 CBSE | 2 Marks | Given the linear equation x – 2y – 6 = 0, write another linear equation in these two variables, such that the geometrical representation of the pair so formed is : i) coincident lines (ii) intersection lines | Class X | IMP Questi

#31 CBSE | 2 Marks | Express 23150 as product of its prime factors. Is it unique ?. | Class X | IMP Question

#30 CBSE | 2 Marks | In the figure, AB and CD are common tangents to two circles of unequal radii. Prove that AB = CD. | Class X | IMP Question

#29 CBSE | 2 Marks | Draw a line segment of length 7 cm and divide it... | Class X | IMP Question

#28 CBSE | 2 Marks | PA and PB are tangents to the circle from an exte... | Class X | IMP Question

#27 CBSE | 2 Marks | Draw a line segment of length 8 cm and divide it... | Class X | IMP Question

#25 and #26 CBSE | 2 Marks | Class X | IMP Question

#47 CBSE | 2 Marks | The x-coordinate of a point P is twice its y-coordinate. If P is equidistant from Q(2, – 5) and R(– 3, 6), find the coordinates of P | Class X | IMPORTANT

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