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5. In the following diagram, we have two non-intersecting circles with centres O₁ and O₂, and radii r1 and r2 respectively. Tangents are drawn from the centre of each circle to the circumference of the other as shown, creating points T₁, W₁, T2, and W₂. The tangents to the first circle intersect the second at X and Y, while the tangents to the second circle intersect the first at P and Q. (a) (b) Show that the line O₁O₂ bisects PQ and XY. Show that PQ = XY T₁ W₁ P X T₂ W₂ 0₂

5. In the following diagram, we have two non-intersecting circles with centres O₁ and O₂, and radii r1 and r2 respectively. Tangents are drawn from the centre of each circle to the circumference of the other as shown, creating points T₁, W₁, T2, and W₂. The tangents to the first circle intersect the second at X and Y, while the tangents to the second circle intersect the first at P and Q. (a) (b) Show that the line O₁O₂ bisects PQ and XY. Show that PQ = XY T₁ W₁ P X T₂ W₂ 0₂

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter6: Circles
Section6.3: Line And Segment Relationships In The Circle
Problem 5E: Sketch two circles that have: a No common tangents b Exactly two common tangents c Exactly three...
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5. In the following diagram, we have two non-intersecting circles with centres O₁ and O₂, and radii 7₁ and r2 respectively. Tangents are drawn from the centre of each circle to the circumference of the other as shown, creating points T₁, W₁, T2, and W₂. The tangents to the first circle intersect the second at X and Y, while the tangents to the second circle intersect the first at P and Q. (a) (b) Show that the line 0₁0₂ bisects PQ and XY. Show that PQ = XY T₁ 0₁ W₁ P X T₂ W₂ -0₂
Transcribed Image Text:5. In the following diagram, we have two non-intersecting circles with centres O₁ and O₂, and radii 7₁ and r2 respectively. Tangents are drawn from the centre of each circle to the circumference of the other as shown, creating points T₁, W₁, T2, and W₂. The tangents to the first circle intersect the second at X and Y, while the tangents to the second circle intersect the first at P and Q. (a) (b) Show that the line 0₁0₂ bisects PQ and XY. Show that PQ = XY T₁ 0₁ W₁ P X T₂ W₂ -0₂
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