Q)27,28,29,30 with steps

Asked by saketagarwal.dbl | 3rd Dec, 2016, 10:13: PM

Expert Answer:

Question 27 solution:
begin mathsize 20px style We space know space that comma space if space QP space and space PR space are space two space equal space chords space of space straight a space circle comma space
so comma space in space increment QPR comma space angle RQP equals angle QRP
then space the space centre space of space the space circle space lies space on space the space bisector space of space angle QPR. space space
Here comma space QP equals PR space equals space 5 space cm. space
So comma space the space bisector space of space angle QPR space passes space through space the space centre space straight O space
straight i. straight e. space OP space is space the space bisector space of space angle QPR. space space
Since space the space internal space bisector space of space an space angle space divides space the space opposite space side space in space the space ratio space
of space the space sides space containing space the space angle. space
Therefore comma space straight M space divides space QR space in space the space ratio space 5 colon 5 space equals space 1 colon 1 space.... left parenthesis Angle space Bisector space Theorem right parenthesis
straight i. straight e. space straight M space is space the space mid minus space point space of space QR. space
Now comma space straight M space is space the space mid space – space point space of space QR. space space space space space space
OM space perpendicular space QR space space
In space the space right space space triangle space OQM comma space
we space have space space OQ squared space equals space OM squared space plus space QM squared space rightwards double arrow OQ squared space equals space left parenthesis OP minus PM right parenthesis squared space plus space QM squared space
rightwards double arrow 36 space equals space left parenthesis 6 minus PM right parenthesis squared space plus space QM squared space
rightwards double arrow QM squared space equals space 36 minus left parenthesis 6 minus PM right parenthesis squared space space.... left parenthesis straight i right parenthesis
In space the space right space triangle space PQM comma space we space have space space space space space space space space
PQ squared space equals space PM squared space plus space QM squared space space
rightwards double arrow 25 space equals space PM squared space plus space QM squared space space space
rightwards double arrow QM squared space equals space 25 minus PM squared space space space space space space.... left parenthesis ii right parenthesis
From space equation space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis comma space
we space get space 36 minus left parenthesis 6 minus PM right parenthesis squared space equals space 25 minus PM squared
36 minus 36 plus 12 PM minus PM squared equals space 25 minus PM squared space space space space space
1 2 PM equals space 25 space space space space space space space space
PM equals space 2.083 space space space
Putting space PM space equals space 2.0833 space space in space equation space left parenthesis ii right parenthesis comma space
we space get space QM squared space equals space 25 minus open parentheses 2.083 close parentheses squared space
rightwards double arrow QM equals space square root of 25 minus 4.338889 end root almost equal to 20.66 space cm
So comma space QR equals 2 QM equals 2 open parentheses 20.66 close parentheses equals 41.32 space cm end style
Kindly post only one question per query.

Answered by Rebecca Fernandes | 5th Dec, 2016, 02:23: PM