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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 = 40degree and ∠ABD = 60degree, find: i) ∠DBC ii) ∠BCP
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 = 40degree and ∠ABD = 60degree, find: i) ∠DBC ii) ∠BCP
Class 10 | Exercise 18C | ICSE | Maths | Selina | Tangents and Intersecting Chords
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 = 40degree and ∠ABD = 60degree, find: i) ∠DBC ii) ∠BCP

Selina Solutions Concise Class 10 Maths Chapter 18 ex. 18(C) - 16

Solution:

15.

(i) \[PQ\]is a tangent and \[CD\]is a chord.

\[\angle DCQ\text{ }=\angle DBC\] [Angles in the alternate segment]

\[\angle DBC\text{ }=\text{ }{{40}^{o}}\]

\[[As\angle DCQ\text{ }=\text{ }{{40}^{o}}]\]

 

(ii) \[\angle DCQ\text{ }+\angle DCB\text{ }+\angle BCP\text{ }=\text{ }{{180}^{o}}\]

\[{{40}^{o}}~+\text{ }{{90}^{o}}~+\angle BCP\text{ }=\text{ }{{180}^{o}}~\]

\[[As\angle DCB\text{ }=\text{ }{{90}^{o}}]\]

\[\angle BCP\text{ }=\text{ }{{180}^{o}}-\text{ }{{130}^{o}}~\]

So,

\[=\text{ }{{50}^{o}}\]

i

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