In the figure- O is the centre of the circle- Find the length of CD-A- 4 cmB- 10 cmC- 5 cmD- 3 cm

The correct option is C 5 cmIn nbsp;s AOB and COD, OA=OC nbsp; nbsp;(radius of the circle), OB=OD nbsp; nbsp;(radius of the circle) nbsp; and ∠ A ...

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Standard IX

Mathematics

Theorem of Equal Angles Subtended by Different Chords

In the figure...

Question

In the figure, O is the centre of the circle. Find the length of CD, if AB=5 cm.

5 cm

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3 cm

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4 cm

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10 cm

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Solution

The correct option is A 5 cm
In $△ s$ AOB and COD,
OA=OC (radius of the circle),
OB=OD (radius of the circle) and
$∠ A O B = ∠ C O D (= 55^{\circ}) .$
$∴$ By SAS congruency, $△ A O B ≅ △ C O D .$
$⟹ A B = C D$ (Corresponding parts of congruent triangles)
Since AB=5 cm, we have CD=5 cm.

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In the figure, O is the centre of the circle. Find the length of CD, if AB=5 cm.

The correct option is A 5 cmIn △s AOB and COD, OA=OC (radius of the circle), OB=OD (radius of the circle) and ∠AOB=∠COD (=55∘). ∴ By SAS congruency, △AOB≅△COD. ⟹AB=CD (Corresponding parts of congruent triangles) Since AB=5 cm, we have CD=5 cm.