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Since PQ is tangent to the circle at R, PO bisects the angles at ∠ EOR. Thus, EOP = POR = θ 1 (let) QO bisects the angle at FOR. Thus, FOQ = QOR = θ ₂ (let) Since AB and CD are parallel tangents to the circle, EF must be a straight line. Thus, from the diagram, ∠ EOP + POR + FOQ + QOR = 180° 2 ( θ 1 + θ 2 ) = 180° ( θ 1 + θ 2 ) = 90° ∠ EOP = 90°
The ratio of the speed of the stream to the speed of the boat in still water is 3:7. If a distance of 280 km is covered downstream in 4 hours, determine...
If 50 less had applied and 25 less selected, the ratio of selected to unselected would have been 9 : 4. So how many candidates had applied if the ratio ...
Three positive numbers are in the 5:6: 7 ratio and the sum of their squares is 13,310. Find the sum of the three numbers
The number of students in class IX and class X is 42 and 45, respectively. The ratio of the number of boys to girls in classes is IX and X is 9: 5 and 8...
The incomes of A and B are in the ratio of 3:2 and their expenditures are Rs. 14,000 and Rs. 10,000 respectively. If A saves Rs. 7000, then B's savings ...
A certain amount was divided among four people P, Q, R and S such that the amount obtained by S is 12.5% more than the amount obtained by Q. The amount ...
28 percent of a number and 40 percent of another number are in the ratio 7: 8. What is the ratio of 50 percent of the first number to 75 percent of the ...
How should the total amount be divided among individuals Mohit, Neeti, Ojesh, and Puneet in the respective proportions of 4:5:7:6, if Ojesh receives Rs....
The ratio of A's income to savings is 25:9, and B's expenditure is 60% of A's total income. If B's expenditure exceeds its savings by Rs. 3500, and A's ...
The ratio of two numbers 'a' and 'b' is 6:2, respectively. Whereas the ratio of 'b' and 'c' is 10:11, respectively. When 14 is added to 'a', it becomes ...
