1. Let C be a circle of radius $$\sqrt{20}$$ cm. Let L1, L2 be the lines given by 2x − y −1 = 0 and x + 2y−18 = 0, respectively. Suppose that L1 passes through the center of C and that L2 is tangent to C at the point of intersection of L1 and L2. If (a,b) is the center of C, which of the following is a possible value of a + b?
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By: anil on 05 May 2019 03.05 pm
As mentioned in the question, Lines L1 and L2 intersect at point P as shown in the figure. On solving for x and y from equations x + 2y - 18 = 0 2 - y - 1 = 0 We get x = 4 and y =7. Given, radius = $$sqrt{20}$$ Using the equation of a circle, we have $$(4-a)^{2}$$ + $$(7-b)^{2}$$ = 20
The only possible solution is 16 and 4. Case 1: $$(4-a)^{2}$$ = 16 & $$(7-b)^{2}$$ = 4
Possible values of a = 0,8 and b= 5,9 in any order Possible sum values = 5,9,13 & 17 Case 2: $$(4-a)^{2}$$ = 4 & $$(7-b)^{2}$$ = 16
Possible values of a = 2,6 and b= 3,11 in any order Possible sum values = 5,9, 13 & 17
From the given options only B satisfies. Hence, option B.
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The only possible solution is 16 and 4. Case 1: $$(4-a)^{2}$$ = 16 & $$(7-b)^{2}$$ = 4
Possible values of a = 0,8 and b= 5,9 in any order Possible sum values = 5,9,13 & 17 Case 2: $$(4-a)^{2}$$ = 4 & $$(7-b)^{2}$$ = 16
Possible values of a = 2,6 and b= 3,11 in any order Possible sum values = 5,9, 13 & 17
From the given options only B satisfies. Hence, option B.