Question
Two circles of radius 13 cm and 15 cm intersect each
other at points A and B. If the length of the common chord is 12 cm, then what is the distance between their centres?Solution
Let O and R be the center of the circle and PQ be the length of the common chord. OP = 15, RP = 13 PS = 1/2 PQ (as perpendicular from the center of the circle to a chord bisects the chord) PS = 1/2 Γ 12 PS = 6 By applying Pythagoras theorem in PSO: OS2 = OP2-PS2 = 152 β 62 = 225-36 = 189 Β OS = β189 Β By applying Pythagoras' theorem in PSO': RSΒ² = RP2-PS2 = 132 - 62 = 169-36 = 133 RS = β133 OR = OS + RS = β189 + β133 The distance between their centers = β189 + β133
The volume and height of a cylinder are 2662 cm3 and 7 cm. Find the radius of the cylinder.
A sphere of the greatest possible size is enclosed within a cube whose edge length is 28 cm. Calculate the surface area (in cmΒ²) of the sphere. (Take οΏ½...
The sum of length, breadth and height of cuboid is 25cm.If the length of the diagonal is 15 cm, then find the total surface area of the cuboid. (in cm <...
ABC is an equilateral triangle with sides of 42cm. Find the difference between its in-radius and circum-radius.
What is the difference between (in m2) the area of a circular field of radius 35 metres and area of a rectangular piece of land having its di...
The ratio of the breadth to the length of a rectangular field is 2:3. The total cost of cutting the grass of the field at the rate of Rs 6 per m2
In measuring the sides of a rectangle, there is an excess of 14% on one side and 10% deficit on the other. Then the error percent in the area is
Two cylindrical buckets 'A' and 'B' are such that the radius of bucket 'A' is thrice that of bucket 'B' whereas the height of bucket 'A' is twice that o...
The average cost of two chairs is Rs. 15000. The average cost decrease by 30% when one more chair is included. What is the cost price of the 3 rd <...
If the area of a rhombus is 14504 mΒ² and the ratio of the diagonals is 37:49 then find the length of the shorter diagonal.
Relevant for Exams:
