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In the given figure, O is the centre of ...

In the given figure, O is the centre of a circle . Prove that
`/_x + /_ y = /_ z`.

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In `Delta ACF`, side CF is produced to B.
`:. /_ y = /_1+ /_ 3` [ ext. `/_ =` sum of int. opp. `Delta s` ] …..(i)
In `Delta AED`, side ED is produced to B.
`:. /_1 + /_ x = /_ 4` ….(ii)
From (i) and(ii) , we have
`/_ 1 + /_ x+/_ y = /_ 1 +/_3 +/_4`
`implies /_x+/_y =/_3 +/_4`
`=2/_3" " [:' /_ 4 = /_ 3` angles in the same segment ]
`= /_z " " [:' /_ AOB = 2 /_ ACB]`.
Hence, `/_ x + /_ y = /_z`.
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RS AGGARWAL-CIRCLES -MULTIPLE CHOICE QUESTION(MCQ)
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  7. In the given figure, CD is the diameter of a circle with centre O and...

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  9. In the given figure, BOC is a diameter of a circle with centre O . If ...

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  10. In the given figure, AB is a chrod of a circle with centre O and AB is...

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  11. In the given figure, AB is a chord of a circle with centre O and BOC i...

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  12. In the given figure, Delta ABC and Delta DBC arre inscribed in a circ...

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  13. In the given figure, BOC is a diameter of a circle with centre O. If /...

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  14. In the given figure, O is the centre of a circle . If / OAC = 50^(@) t...

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  15. In the given figure, O is the centre of a circle in which / OBA = 20^(...

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  16. In the given figure, O is the centre of a circle. If / AOB = 100^(@) a...

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  17. In the given figure, O is the centre of a circle . The, / OAB = ?

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  18. In the given figure, O is the centre of a circle and / AOC = 120^(@) ....

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  19. In the given figure, O is the centre of a circle and / OAB=50^(@). The...

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  20. In the given figure, AB and CD are two intersecting chords of acircle...

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  21. In the given figure, O is the centre of a circle and chords AC and BD ...

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