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 × 12 PS = 6 By applying Pythagoras theorem in PSO: OS2 = OP2-PS2 = 152 – 62 = 225-36 = 189 OS = √189 By applying Pythagoras' theorem in PSO': RS² = RP2-PS2 = 132 - 62 = 169-36 = 133 RS = √133 OR = OS + RS = √189 + √133 The distance between their centers = √189 + √133
P can do a piece of work in 15 days, Q can complete double the work in 40 days and R can do the work in 20 days. If all of them together earn Rs. 3000, ...
- Alex and Ben can complete a job individually in 14 days and 21 days, respectively. If they take turns to work one day each, beginning with Alex, how long w...
‘X’ and ‘Y’ can do a task together in 15 days. If ‘X’ alone takes 25 days to complete it, then how much time will ‘Y’ take to finish the...
‘P’ and ‘Q’ can complete a task together in 24 days. If ‘P’ alone can do it in 40 days, find the number of days ‘Q’ alone will take to f...
A can complete a work in 40 days. B takes 20 days less than A to complete the same work. In how many days can both of them together complete 90% of the ...
P can do a piece of work in 30 days. Q do the same work in 40 days. R can do it in 35 days. P and R worked for 4 days and handed it to Q. Q worked for s...
X can do a piece of work in 15 days. He worked at it for 3 days and then Y finished it in 16 days. In how many days can X and Y together finish the work?
A job is done by 15 men in 30 days and 30 women in 20 days. How many days will it take for 8 men and 12 women to finish the work?
P can do a piece of work in 20 days, Q can do the same piece of work in 24 days while R can do it in 30 days. They started working together but after 4 ...
12 engineers complete designing 180 blueprints in 15 days. If the goal is to complete 270 blueprints in 18 days, how many engineers are required?
Relevant for Exams:
