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From the above figure we get that AC = AB + BC BD = BC + CD It is given that AC = BD Plug the value of AC we get AB + BC = BC + CD … (1) According to Euclid’s axiom,when equals are subtracted from equals, the remainders are also equal. Subtracting BC from both side in equation (1), we get AB + BC − BC = BC + CD − BC AB = CD Hence proved
We can see that the ratio can be used to find the factor So perimeter of triangle =a+b+c This gives 12x+13x+5x=450 Thus x= 450/30 X= 15 So A=12 ×15=180 B=5×15=75 C=13×15=195 We know that 12:5:13 is a Pythagorean triplet. Hence the triangle here is a right angle triangle with base 5x and height 12x or vice versa and hypotenuse is 13x Thus we can use Area= 1/2(base *height) Area = 1/2(180*75) = 6750 m²
Mr.A has x children while Mrs.B has (x+1) children. After they got married, totally they have 10 children. But it is not given how many children do they have after they got married. Let they be 'y'. Then, we get, x+(x+1)+y=10 i.e. 2x+y=9. Here, if y can take only odd values, otherwise, x will not be a positive integer for any even value of y. Then there are following cases: 1) for y=1, x=4 and x+1=5, 2) for y=3, x=3 and x+1=4 3) for y=5, x=2 and x+1=3 4) for y=7, x=1 and x+1=2 5) for y=9, x=0 and x+1=1. As the children of same parents cannot quarrel, only y can quarrel with x and (x+1) and x can quarrel with (x+1). Then from above five cases, we have to consider the case which will give maximum value. It is the the 2nd case. That is, the product xy+y(x+1)+x(x+1) will be maximum for y=3, x=3 and (x+1)=4, that is 33. Hence 33 is the answer.
OPTION A 33
THE ANSWER IS OPTION C, HERE YOU CAN SEE THE SOLUTION IN THE IMAGE BELOW!
join OP, OQ and OX
using RHS we can show triangle POX and QOX are congruents and hence XP=XQ.
so basically if X is an external point and XP and XQ be two tangents from X to a circle then XP=XQ.
using the same logic for external point A we can show AP=AR as AP and AR are tangents o the circle from external point A
and similarly for external point B we have BR=BQ
so XA+AR= XA+AP = XP
and XB+BR= XB+BQ= XQ
XP=XQ (FROM ABOVE)
so XA+AR= XP= XQ = XB+BR
The given number series is based on the following pattern :
Hence , 10.75 will replace the question mark
When you mix magnesium with hydrochloric acid, the hydrochloric acid dissolves the magnesium and produces Hydrogen gas. The less concentrated the hydrochloric acid is, the slower the magnesium dissolves. If the hydrochloric acid is mixed with the magnesium, then it will result in a chemical change