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3. Two chords of a circle AB and CD intersect at X. B Use similar triangles to prove that AX.BX = CX.DX. This result is called the Intersecting Chords Theorem.

3. Two chords of a circle AB and CD intersect at X. B Use similar triangles to prove that AX.BX = CX.DX. This result is called the Intersecting Chords Theorem.

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.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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374 Using and applying mathematics 3. Two chords of a circle AB and CD intersect at X. B Use similar triangles to prove that AX.BX = CX.DX. This result is called the Intersecting Chords Theorem. A D 4. Line ATB touches a circle at T and TC is a diameter. AC and BC cut the circle at D and E respectively. Prove that the quadrilateral ADEB is cyclic. 5. Prove that the angle in a semicircle is a right angle. 6. TC is a tangent to a circle at C and BA produced meets this tangent at T. Show that triangles TCA and TBC are similar and hence prove that TC? = TA x TB. 7. Given that BOC is a diameter and that ADC = 90°, prove that AC bisects BCD. E 10.4 Coursework tasks EK
Transcribed Image Text:374 Using and applying mathematics 3. Two chords of a circle AB and CD intersect at X. B Use similar triangles to prove that AX.BX = CX.DX. This result is called the Intersecting Chords Theorem. A D 4. Line ATB touches a circle at T and TC is a diameter. AC and BC cut the circle at D and E respectively. Prove that the quadrilateral ADEB is cyclic. 5. Prove that the angle in a semicircle is a right angle. 6. TC is a tangent to a circle at C and BA produced meets this tangent at T. Show that triangles TCA and TBC are similar and hence prove that TC? = TA x TB. 7. Given that BOC is a diameter and that ADC = 90°, prove that AC bisects BCD. E 10.4 Coursework tasks EK
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