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ICSE Class 10 Mathematics Question 21 of 28

Short Answer Questions 1 — Question 21

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Question 70

AB and CD intersect at the center O of the circle given in the above diagram. If ∠EBA = 33° and ∠EAC = 82°, find

(a) ∠BAE

(b) ∠BOC

(c) ∠ODB

AB and CD intersect at the center O of the circle given in the above diagram. If ∠EBA = 33° and ∠EAC = 82°, find . Maths Competency Focused Practice Questions Class 10 Solutions.
Answer

(a) In △ BAE,

⇒ ∠AEB = 90° (Angle in a semicircle is a right angle)

By angle sum property of triangle,

⇒ ∠AEB + ∠EBA + ∠BAE = 180°

⇒ 90° + 33° + ∠BAE = 180°

⇒ ∠BAE + 123° = 180°

⇒ ∠BAE = 180° - 123° = 57°.

Hence, ∠BAE = 57°.

(b) From figure,

⇒ ∠EAC = ∠EAB + ∠BAC

⇒ 82° = 57° + ∠BAC

⇒ ∠BAC = 82° - 57° = 25°.

We know that,

The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

⇒ ∠BOC = 2∠BAC = 2 × 25° = 50°.

Hence, ∠BOC = 50°.

(c) From figure,

∠BOC and ∠BOD form a linear pair.

∴ ∠BOC + ∠BOD = 180°

⇒ 50° + ∠BOD = 180°

⇒ ∠BOD = 180° - 50° = 130°.

In △ BOD,

⇒ ∠BOD + ∠ODB + ∠DBO = 180°

⇒ 130° + ∠ODB + 33° = 180°

⇒ ∠ODB + 163° = 180°

⇒ ∠ODB = 180° - 163° = 17°.

Hence, ∠ODB = 17°.