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In the following figure seg AB ⊥ seg BC, seg DC ⊥ seg BC. If AB = 2 and DC = 3, find `(A(triangleABC))/(A(triangleDCB))`

If two circles with radii 5 cm and 3 cm respectively touch internally, find the distance between their centres.

Find the slope of the line passing through the points A(-2, 1) and B(0, 3).

Find the area of the sector whose arc length and radius are 8 cm and 3 cm respectively.

In the following figure, Q is the centre of a circle and PM, PN are tangent segments to the circle. If ∠MPN = 50°, find ∠MQN.

Draw the tangents to the circle from the point L with radius 2.7 cm. Point ‘L’ is at a distance 6.9 cm from the centre ‘M’.

The ratio of the areas of two triangles with the common base is 14 : 9. Height of the larger triangle is 7 cm, then find the corresponding height of the smaller triangle.

Two building are in front of each other on either side of a road of width 10 metres. From the top of the first building which is 40 metres high, the angle of elevation to the top of the second is 45°. What is the height of the second building?

Find the volume and surface area of a sphere of radius 2.1 cm.

`(pi=22/7)`

Prove that ‘the opposite angles of a cyclic quadrilateral are supplementary’.

A test tube has diameter 20 mm and height is 15 cm. The lower portion is a hemisphere. Find the capacity of the test tube. (π = 3.14)

Prove that the angle bisector of a triangle divides the side opposite to the angle in the ratio of the remaining sides.

Write down the equation of a line whose slope is 3/2 and which passes through point P, where P divides the line segment AB joining A(-2, 6) and B(3, -4) in the ratio 2 : 3.

ΔRST ~ ΔUAY, In ΔRST, RS = 6 cm, ∠S = 50°, ST = 7.5 cm. The corresponding sides of ΔRST and ΔUAY are in the ratio 5 : 4. Construct ΔUAY.