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ff Two circles with centers A and B intersect at M and N. m∠P = 72, m∠S = 80. Find m∠Q. ff

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ff Two secants drawn from the same point to a circle make intercepted arcs in the ratio 2 : 5. What is the ratio of the measure of the angle between the secants to the measure of the intercepted arcs? ff

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ff Two tangents drawn to a circle from a point are at right angles to each other. What are the measures of the intercepted arcs? ff

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ff Two tangents drawn from the same point makes an angle equal to the measure of that of one of the intercepted arcs. Find the measure of the angle between the tangents. ff

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ff Ratio of the two intercepted arcs made by two secants drawn from the same point to a circle is 1 : 2. What is the ratio of the measure of the angle between the secants to the measure of the smaller intercepted arc? ff

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ff Two secants drawn from the same point to a circle make an angle of 30° between them. If the measure of the smaller intercepted arc made by the secants is 50°, then find the measure of the larger intercepted arc. ff

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ff Chords AB¯ and CD¯ of a circle intersect at E. Measure of arc AC = 60°, m∠AEC = 80°. Find the measure of arc BD. ff

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ff In a circle, the angle between 2 secants drawn from the same point to a circle is found to be one third of the larger intercepted arc. If the measure of the smaller intercepted arc is 30°, then what is the measure of the angle between the secants? ff

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ff Is it possible that the measure of the larger intercepted arc made by two secants drawn from the same point to a circle is 2 times the angle between the secants? ff

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ff Is it possible that the measure of the angle between the two secants drawn from the same point to a circle is equal to the measure of the smaller intercepted arc? ff

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ff Two chords AB¯ and CD¯ of a circle intersect at E. The smaller angle between the chords is 70°. The measures of the corresponding intercepted arcs are in the ratio 3 : 2. Find the measures of the intercepted arcs AC and BD. ff

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ff Four chords AB¯, CD¯, AE¯ and CF¯ intersect. m∠ANC = 40, measure of arc BD = 30. If m∠AMC = 45(m∠ANC), then find the measure of arc EF. ff

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ff The ratio of the measure of the larger intercepted arc made by two secants (drawn from the same point to a circle) to the measure of the angle between the secants is 4 : 1. If the smaller intercepted arc measures 50°, then find the measure of the larger intercepted arc and the measure of the angle between the secants. ff

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ff What is the condition that the angle between two secants drawn from the same point to a circle becomes equal to one of the intercepted arcs? ff

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ff A tangent is drawn from point A to a circle. A secant is also drawn from A such that it makes 30° with the tangent. If the measure of the smaller intercepted arc of the circle is 40°, then what is the measure of the larger intercepted arc (y)? ff

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ff The measure of the angle between a tangent and a secant drawn to a circle from the same point is 60. The point of tangency and one of the points of intersection of the circle and the secant from the end points of a diameter of the circle. Find the measures of the intercepted arcs made by the secant and the tangent. ff

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ff OA→ and OB→ are tangents to the circle. Find the value of x. ff

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ff CA→ and CB→ are tangents. Measure of the major arc AB = 240, m∠ACB = ? ff

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ff Chords PQ¯ & RS¯ of a circle intersect at O.mPR = 2(mSQ), m∠SOQ = 60°. Find the measure of arc PR. ff

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ff Smaller angle between two diameters of a circle is 20°. Measure of larger intercepted arc is ff

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ff ΔPQR is inscribed in the circle with center 'O'. Find m∠A + m∠B + m∠C. ff

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ff Two circles with centers A and B intersect at M and N. m∠P = 75, m∠S = 83. Find m∠Q. ff

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