List of top Mathematics Questions on Geometry asked in AP EAMCET

If a variable straight line passing through the point of intersection of the lines x - 2y + 3 = 0 and 2x - y - 1 = 0 intersects the X and Y axes at A and B respectively, then the equation of the locus of a point which divides the segment AB in the ratio -2 : 3 is:
In a triangle ABC, if \( (r_1 + r_2) \csc^2 \frac{C}{2} = \)
If \( H \) is the orthocenter of \( \triangle ABC \) and \( AH = x \), \( BH = y \), \( CH = z \), then evaluate: \[ \frac{abc}{xyz} \]
In a triangle ABC, if \( r : R = 1 : 3 : 7 \), then \( \sin(A + C) + \sin B = \)
Find the locus of points satisfying the equation \( axy + byz = cy \).
If a running track of 500 ft. is to be laid out enclosing a playground, the shape of which is a rectangle with a semicircle at each end, then the length of the rectangular portion such that the area of the rectangular portion is maximum is (in feet).
In a triangle ABC, if \( a = 13, b = 14, c = 15 \), then \( r_1 = \)
In \(\Delta ABC\) if \(B = 90^\circ\) then \(2(r + R) = \)
In a triangle ABC, if \( (a-b)(s-c) = (b-c)(s-a) \), then \( r_1 + r_3 = \):
In \( \triangle ABC \), given: \[ a = 26, \quad b = 30, \quad \cos C = \frac{63}{65} \] Find \( c \).
If the angle \( \theta \) between the line \( \frac{x + 1}{1} = \frac{y - 1}{2} = \frac{z - 2}{2} \) and the plane \( 2x - y + \sqrt{\lambda}z + 4 = 0 \) is such that \( \sin \theta = \frac{1}{3} \), then the value of \( \lambda \) is:
If the direction cosines of two lines are given by \[ l + m + n = 0 \quad \text{and} \quad mn - 2lm - 2nl = 0, \] then the acute angle between those lines is: