Geometry (C10)
Triangles and Circles
Area of a triangle whose vertices are (1, -1) (-4, 6) and (-3, -5)
Find the area of a triangle whose vertices are given as (1, -1) (-4, 6) and (-3, -5).
Read more …Find a relation between x and y if the points A(x, y), B(-4, 6) and C(-2, 3)
Find a relation between x and y if the points A(x, y), B(-4, 6) and C(-2, 3) are collinear.
Read more …In given figure ∠1 = ∠2 and ΔNSQ ≅ ΔMTR , then prove that ΔPTS ~ ΔPRQ
In given figure ∠1 = ∠2 and ΔNSQ ≅ ΔMTR , then prove that ΔPTS ~ ΔPRQ.
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Two right triangles ABC and DBC are drawn on the same hypotenuse
Two right triangles ABC and DBC are drawn on the same hypotenuse BC and on the same side of BC. If AC and BD intersect at P, prove that AP × PC = BP × DP.
Read more …Diagonals of a trapezium PQRS intersect each other at the point O
Diagonals of a trapezium PQRS intersect each other at the point O, PQ ∥ RS and PQ = 3RS. Find the ratio of the areas of triangles POQ and ROS.
Read more …In Figure, PQ and RS are two parallel tangents to a circle with centre O
In Figure, PQ and RS are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting PQ at A and RS at B. Prove that ∠AOB = 90º.
Read more …Find the ratio in which the line x – 3y = 0 divides the line segment
Find the ratio in which the line x – 3y = 0 divides the line segment joining the points (–2, –5) and (6, 3). Find the coordinates of the point of intersection.
Read more …X is a point on the side BC of ΔABC. XM and XN are drawn parallel
X is a point on the side BC of ΔABC. XM and XN are drawn parallel to AB and AC respectively meeting AB in N and AC in M. MN produced meets CB produced at T. Prove that TX2 = TB × TC
Read more …In Figure, ABC is a triangle in which ∠B = 90º, BC = 48 cm and AB = 14 cm
In Figure, ABC is a triangle in which ∠B = 90º, BC = 48 cm and AB = 14 cm. A circle is inscribed in the triangle, whose centre is O. Find radius r of in-circle.
Read more …Find the linear relation between x and y such that P(x, y) is equidistant
Find the linear relation between x and y such that P(x, y) is equidistant from the points A(1, 4) and B(–1, 2).
Read more …If coordinates of two adjacent vertices of a parallelogram are (3, 2), (1, 0)
If coordinates of two adjacent vertices of a parallelogram are (3, 2), (1, 0) and diagonals bisect each other at (2, –5), find coordinates of the other two vertices.
Read more …If the area of triangle with vertices (x, 3), (4, 4) and (3, 5) is 4 square units
If the area of triangle with vertices (x, 3), (4, 4) and (3, 5) is 4 square units, find x.
Read more …In figure, AB is a chord of length 8 cm of a circle of radius 5 cm
In figure, AB is a chord of length 8 cm of a circle of radius 5 cm. The tangents to the circle at A and B intersect at P. Find the length of AP.
Read more …Prove that the ratio of the areas of two similar triangles is equal to
Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.
Read more …Find the ratio in which P(4, m) divides the line segment
Find the ratio in which P(4, m) divides the line segment joining the points A(2, 3) and B(6, –3). Hence find m.
Read more …If A(–5, 7), B(–4, –5), C(–1, –6) and D(4, 5) are the vertices of a quadrilateral
If A(–5, 7), B(–4, –5), C(–1, –6) and D(4, 5) are the vertices of a quadrilateral, find the area of the quadrilateral ABCD.
Read more …If A(–2, 1), B(a, 0), C(4, b) and D(1, 2) are the vertices of a parallelogram ABCD
If A(–2, 1), B(a, 0), C(4, b) and D(1, 2) are the vertices of a parallelogram ABCD, find the values of a and b. Hence find the lengths of its sides.
Read more …Prove that the area of an equilateral triangle described on one side of the square
Prove that the area of an equilateral triangle described on one side of the square is equal to half the area of the equilateral triangle described on one of its diagonal.
Read more …If the area of two similar triangles are equal, prove that they are congruent
If the area of two similar triangles are equal, prove that they are congruent.
Read more …Find the area of the shaded region, where arcs drawn with centres A, B, C and D intersect
Find the area of the shaded region in Figure, where arcs drawn with centres A, B, C and D intersect in pairs at mid-points P, Q, R and S of the sides AB, BC, CD and DA respectively of a square ABCD of side 12 cm. [Use π = 3.14]
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In an equilateral triangle ABC, D is a point on the side BC
In an equilateral triangle ABC, D is a point on the side BC such that BD = 1/3 BC. Prove that 9AD2 = 7AB2
Read more …If the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k - 1, 5k) are collinear
If the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k - 1, 5k) are collinear, then find the value of k.
Read more …Show that in a right triangle, the square of the hypotenuse is equal to
Show that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Read more …In given figure XY and X'Y' are two parallel tangents to a circle
In given figure XY and X'Y' are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and X'Y' at B. Prove that ∠ AOB = 90°.
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The points A(4, –2), B(7, 2), C(0, 9) and D(–3, 5) form a parallelogram
The points A(4, –2), B(7, 2), C(0, 9) and D(–3, 5) form a parallelogram. Find the length of the altitude of the parallelogram on the base AB.
Read more …In what ratio does the x-axis divide the line segment joining the points (–4, –6) and (–1, 7)
In what ratio does the x-axis divide the line segment joining the points (–4, –6) and (–1, 7)? Find the co-ordinates of the point of division.
Read more …If (1, p/3) is the mid-point of the line segment joining the points (2, 0) and (0, 2/9)
If (1, p/3) is the mid-point of the line segment joining the points (2, 0) and (0, 2/9), then show that the line 5x + 3y + 2 = 0 passes through the point (–1, 3p).
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