Two circles `C_1` and `C_2` intersect at two distinct points `P`and`Q` in a line passing through `P` meets circles `C_1`and`C_2` at `A`and`B` , respectively. Let `Y` be the midpoint of `A B` and `Q Y` meets circles `C_1` and`C_2` at `X`a n d`Z` respectively. Then prove that `Y` is the midpoint of `X Z`

Two circles intersects at point C and D. Straight lines through C and D meet two circles at B and F, and A and E respectively. If angleDAB = 75^@ then value of the PM angleDEF is balchera

Two circles intersect each other at the points P and Q. Two straight lines through P and Q intersect on circle at the points A and C and the other circle at B and D . Prove that AC||BD.

Two circles intersect each other at the points P and Q. A straight line passing through P intersects one circle at A the other circle at .A straight line passing through Q intersect the first circle at C and the second circle at D. Prove that AC||BD .

Consider two lines L_1a n dL_2 given by a_1x+b_1y+c_1=0a n da_2x+b_2y+c_2=0 respectively where c1 and c2 !=0, intersecting at point PdotA line L_3 is drawn through the origin meeting the lines L_1a n dL_2 at Aa n dB , respectively, such that PA=P B . Similarly, one more line L_4 is drawn through the origin meeting the lines L_1a n dL_2 at A_1a n dB_2, respectively, such that P A_1=P B_1dot Obtain the combined equation of lines L_3a n dL_4dot

Ankita drew two circles which intersect each other at the points P and Q. Through the point P two straight lines are draw so that they intersect one of the circle at the points. A and B and the ohte circle at the points C and D respectively. Prove that angle AQC= angle BQD .

The centre of two circle are P and Q they intersect at the points A and B. The straight line parallel to the line segment PQ through the point A intersects the two circles at the point C and D Prove that CD = 2PQ

The tangent at any point P on the circle x^2+y^2=4 meets the coordinate axes at A and B . Then find the locus of the midpoint of A Bdot

The circle with equation x^2 +y^2 = 1 intersects the line y= 7x+5 at two distinct points A and B. Let C be the point at which the positive x-axis intersects the circle. The angle ACB is

The circle C1 : x^2 + y^2 = 3 , with center at O, intersects the parabola x^2 = 2y at the point P in the first quadrant. Let the tangent to the circle C1 at P touches other two circles C2 and C3 at R2 and R3, respectively. Suppose C2 and C3 have equal radii 2sqrt(3) and centers Q2 and Q3, respectively.If Q_2 and Q_3 lies on the y-axis, then find Q_(2)Q_(3)=12 and R_(2)R_(3)=4sqrt(6)