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Byju's Answer

Standard VIII

Mathematics

Angle in a Semicircle

If C 1 and C ...

Question

If C1 and C2 are 2 circles with O and C as centres respectively and AB∥DE, then identify which angle is 50°.

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Solution

The correct option is A
Given that, C1 and C2 are circles with centres O and C respectively.
$\Rightarrow$ AB is the diameter of C1. A triangle inscribed in a semi circle with its diameter as the largest side will always be a right angled triangle.
$\Rightarrow ∠ A C B = 90 °$

Angle subtended by an arc at the centre is double the angle subtended at the circumference.
$∴ ∠ D F E = \frac{1}{2} ∠ D C E = \frac{1}{2} \times 90 ° = 45 °$

Since AB∥DE, $∠ D E C = 40 °$ [CPCT]
$∴$ Using angle sum property in $△ D C E, ∠ E D C = 180 ° - [∠ D E C + ∠ D C E]$
$= 180 ° - [40 ° + 90 °]$
$= 50 °$

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