Solution: According to the given question, \[AC\] is the side of a regular octagon, \[\angle AOC\text{ }=\text{ }{{360}^{o}}/\text{ }8\text{ }=\text{ }{{45}^{o}}\] Hence, \[arc\text{ }AC\]subtends...

Solution: (i) \[Arc\text{ }AB\] subtends\[\angle AOB\]at the centre and \[\angle ACB\]at the remaining part of the circle. \[\angle ACB\text{ }=\text{ }{\scriptscriptstyle 1\!/\!{ }_2}\angle AOB\]...

Join \[OP,\text{ }OQ,\text{ }OR\text{ }and\text{ }OS\] Given, \[PQ\text{ }=\text{ }QR\text{ }=\text{ }RS\] So, \[\angle POQ\text{ }=\angle QOR\text{ }=\angle ROS\] [Equal chords subtends equal...

Solution: Join \[OP,\text{ }OQ,\text{ }OR\text{ }and\text{ }OS\] Given, \[PQ\text{ }=\text{ }QR\text{ }=\text{ }RS\] So, \[\angle POQ\text{ }=\angle QOR\text{ }=\angle ROS\] [Equal chords subtends...

Let ABCD is a cyclic quadrilateral in which\[AB\text{ }||\text{ }DC\] \[AC\text{ }and\text{ }BD\]are its diagonals. Required to prove: \[\left( i \right)\text{ }AD\text{ }=\text{ }BC\] \[\left( ii...

Solution: Join \[AE,\text{ }OB\text{ }and\text{ }OC\] (i) As \[AOD\]is the diameter \[\angle AED\text{ }=\text{ }{{90}^{o}}~\] [Angle in a semi-circle is a right angle] But, given \[\angle DEF\text{...