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In the figure given alongside, AOB is a diameter of the circle and ∠AOC = 110degree, find ∠BDC.

Selina Solutions Concise Class 10 Maths Chapter 17 ex. 17(A) - 19

Solution:

Join \[AD\]

So, we get

\[\angle ADC\text{ }=\text{ }{\scriptscriptstyle 1\!/\!{ }_2}\angle AOC\text{ }=\text{ }{\scriptscriptstyle 1\!/\!{ }_2}\text{ }x\text{ }{{110}^{o}}~=\text{ }{{55}^{o}}\]

[Angle at the centre is double the angle at the circumference subtended by the same chord]

And, we know that

\[\angle ADB\text{ }=\text{ }{{90}^{o}}\]

[Angle in the semi-circle is a right angle]

Hence,

\[\angle BDC\text{ }=\text{ }{{90}^{o}}-\angle ADC\text{ }=\text{ }{{90}^{o}}-\text{ }{{55}^{o}}\]

\[\angle BDC\text{ }=\text{ }{{35}^{o}}\]