Contoh Soal dan Pembahasan Segi Empat Tali Busur Lingkaran - Matematika Kelas XI Kurikulum Merdeka

Summary

The video explains how to solve problems involving cyclic quadrilaterals, whose vertices lie on a circle. It reviews the rule that opposite angles in a cyclic quadrilateral add up to (180^\circ) and combines this rule with the relationship between central and inscribed angles.

Key ideas and worked examples

Finding an opposite angle in a cyclic quadrilateral

In quadrilateral (ABCD), (\angle ABC) and (\angle ADC) are opposite angles, so:

[ \angle ABC+\angle ADC=180^\circ ]

Given (\angle ABC=84^\circ):

[ \angle ADC=180^\circ-84^\circ=96^\circ ]

Combining cyclic-quadrilateral and circle-angle rules

In the second example, the central angle (\angle RPT=124^\circ) and the inscribed angle (\angle RQT) subtend the same arc (RT). A central angle is twice the inscribed angle subtending the same arc:

[ \angle RQT=\frac{124^\circ}{2}=62^\circ ]

In cyclic quadrilateral (QRST), (\angle RQT) and (\angle RST) are opposite angles:

[ \angle RST=180^\circ-62^\circ=118^\circ ]

Practice question

The presenter gives an additional exercise: In a circle with center (O), if (\angle ABC=134^\circ), find (\angle AOC). Viewers are invited to solve it and share their answer in the comments; the video does not provide the solution.

Main lesson

Circle-geometry problems may require combining several related facts. Identify which angles are opposite in a cyclic quadrilateral, and check whether an inscribed angle and a central angle subtend the same arc.

Speakers and sources

• Presenter/narrator: BSMath Channel. No other speakers are featured.