ICSE Class 10CISCE
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In the given figure, ABCD is a cyclic quadrilateral, PQ is tangent to the circle at point C and BD is its diameter. If ∠DCQ = 40° and ∠ABD = 60°, find; (i) ∠DBC (ii) ∠BCP (iii) ∠ADB - ICSE Class 10 - Mathematics

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Question

In the given figure, ABCD is a cyclic quadrilateral, PQ is tangent to the circle at point C and BD is its diameter. If ∠DCQ = 40° and ∠ABD = 60°, find;

(i) ∠DBC (ii) ∠BCP (iii) ∠ADB

Solution

 (i)PQ is tangent and CD is a chord
∴ `∠`DCQ = `∠` DBC (angles in the alternate segment)

DBC = 40° (∵  `∠`DCQ = 40°)

ii)  `∠`DCQ +  `∠`DCB +  `∠`BCP = 180°

⇒ 40° + 90° +  `∠`BCP = 180° (∵ `∠`DCB = 90°)

⇒ `∠`BCP = 180° = 130° = 50°

iii) In Δ ABD 

 `∠`ADB = 180° , `∠`ABD = 60°

∴  `∠`ADB = 180° - ( 90° + 60°)

⇒ `∠`ADB = 180° - 150° = 30°

  Is there an error in this question or solution?

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Solution In the given figure, ABCD is a cyclic quadrilateral, PQ is tangent to the circle at point C and BD is its diameter. If ∠DCQ = 40° and ∠ABD = 60°, find; (i) ∠DBC (ii) ∠BCP (iii) ∠ADB Concept: Cyclic Properties.
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