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In the given figure, O is centre of the larger circle of radius 10 cm while P is the centre of the smaller circle. If AB = 10√2 cm, find the area of segment ABC lying outside the smaller circle.
  • a)
    22.5π – 25
  • b)
    22.5π – 50
  • c)
    45π – 50
  • d)
    45π – 50
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
In the given figure, O is centre of the larger circle of radius 10 cm...
Let OC meet AB at D, as we have right triangle ODB
So, OD2 + DB2 = OB2.
OB = 10, DB =
So, OD= 5√2
Now in triangle ODB, OD=DB and similarly OD=AD.
So, we can say ∠B = ∠DOB = 450
Similarly ∠C = ∠DOC = 450
So, ∠AOB = 900
So, area of sector AOB = 1/4 π (10)2 = 25π
Area of segment ABC = Area of sector AOB - area of triangle OAB = 25π- 1/2 x10 x10
= 25π - 50
Area of segment ABC lying outside smaller circle is area of segment ABC - area of smaller circle
Now for smaller circle diameter is DC and we have OC = OD + DC DC = 10 - 5√2.
So, radius of smaller circle is
So, the required area =
= (25√2 - 12.5) π - 50 = 22.5π – 50.
Hence, the correct option is (b).
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DIRECTIONSfor the question:Read the passage and answer the question based on it.The tale of reading begins when the retina receives photons reflected off the written page. But the retina is not a homogeneous sensor. Only its central part, called the fovea, is dense in high-resolution cells sensitive to incoming light, while the rest of the retina has a coarser resolution. The fovea, which occupies about 15 degrees of the visual field, is the only part of the retina that is genuinely useful for reading. When foveal information is lacking, whether due to a retinal lesion, to a stroke having destroyed the central part of the visual cortex, or to an experimental trick that selectively blocks visual inputs to the fovea, reading becomes impossible."The need to bring words into the fovea explains why our eyes are in constant motion when we read. By orienting our gaze, we "scan" text with the most sensitive part of our vision, the only one that has the resolution needed to determine letters. However, oureyesdo not travel continuously across the page. Quite the opposite: they move in small steps called saccades. At this very moment, you are making four or five of these jerky movements every second, in order to bring new information to your fovea. Even within the fovea, visual information is not represented with the same precision at all points. In the retina as well as in the subsequent visual relays of the thalamus and of the cortex, the number of cells allocated to a given portion of the visual scene decreases progressively as one moves away from the center of gaze. This causes a gradual loss of visual precision. Visual accuracy is optimal at the center and smoothly decreases toward the periphery. We have the illusion of seeing the whole scene in front of us with the same fixed accuracy, as if it were filmed by a digital camera with a homogeneous array of pixels. However, unlike the camera, our eye sensor accurately perceives only the precise point where our gaze happens to land. The surroundings are lost in an increasingly hazy blurrinessOne might think that, under these conditions, it is the absolute size of printed characters that determines the ease with which we can read: small letters should be harder to read than larger ones. Oddly enough, however, this is not the case. The reason is that the larger the characters, the more room they use on the retina. When a whole word is printed in larger letters, it moves into the periphery of the retina, where even large letters are hard to discern. The two factors compensate for each other almost exactly, so that an enormous word and a minuscule one are essentially equivalent from the point of view of retinal precision. Of course, this is only true provided that the size of the characters remains larger than an absolute minimum, which corresponds to the maximal precision attained at the center of our fovea. When visual acuity is diminished, for instance in aging patients, it is quite logical to recommend books in large print .Our eyes impose a lot of constraints on the act of reading. The structure of our visual sensors forces us to scan the page by jerking our eyes around every two or three tenths of a second Reading is nothing but the word-by-word mental restitution of a text through a series of snapshots. file some small grammatical words like "the," "it or "is" can sometimes be skipped, almost all content words such as nouns and verbs have to be fixated at least once.These constraints are an integral part of our visual apparatus and cannot be lifted by training. One can certainly teach people to optimize their eye movements patterns, but most good readers, who read four hundred words per minute, are already close to optimal. Given the retinal sensor at our disposal, it is probably not possible to do much better. A simple demonstration proves that eye movements are the rate-limiting step in reading. If a full sentence is presented, word by word, at the precise point where gaze is focalized, thus avoiding the need for eye movements, a good reader can read five hundred words per minute at staggering speed-a mean of eight hundred words per minute, and up to sixteen hundred words per minute for the best readers, is about one word every forty milliseconds and three to four times faster than normal reading! With this method, called rapid sequential visual presentation, or RSVP, identification and comprehension remain satisfactory, thus suggesting that the duration of those central steps does not impose a strong constraint on normal reading. Perhaps this computerized presentation mode represents the future of reading in a world where screens progressively replace paper.At any rate, as long as text is presented in pages and lines, acquisition through gaze will slow reading and impose an unavoidable limitation. Thus, fast reading methods that advertise gains in reading speed of up to one thousand words per minute or more must be viewed with skepticism. One can no doubt broaden ones visual span somewhat, in order to reduce the number of saccades per line, and it is also possible to learn to avoid moments of regression, where gaze backtracks to the words it has just read. However, the physical limits of the eyes cannot be overcome, unless one is willing to skip words and thus run the risk of a misunderstanding. Woody Allen described this situation perfectly: "I took a speed-reading course and was able to readWar and Peacein twenty minutes. It involves Russia."Q.Why does the author recommend books in larger print for old people?

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In the given figure, O is centre of the larger circle of radius 10 cm while P is the centre of the smaller circle. If AB = 10√2 cm, find the area of segment ABC lying outside the smaller circle.a)22.5π – 25b)22.5π – 50c)45π – 50d)45π – 50Correct answer is option 'B'. Can you explain this answer?
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