Question

Draw a circle and cut it into two segment. Construct two inscribed angles in each of the
segment and measure them.
​

Answer 1

Given :- Draw a circle and cut it into two segment . Construct two inscribed angles in each of the segment and measure them .

Solution :-

we know that,

• A segment of a circle is a region bounded by a chord and a corresponding arc .
• 2 types of segments are :- Minor segment (made by a minor arc) and Major segment .
• Minor segment is made by minor ac and Major segment is made by major arc of the circle .
• Sum of opposite angles of a cyclic quadrilateral is equal to 180° .

so, from image,

• Draw a chord BC .
• Segment between chord and minor arc BDC is minor segment .
• Segment between chord and major arc BAC is major segment .
• Let us assume that, angle inscribed in minor segment is θ .

then,

→ ∠BDC = θ

now, in cyclic quadrilateral ABDC we have,

→ ∠BDC + ∠BAC = 180° { property of cyclic quadrilateral. }

→ θ + ∠BAC = 180°

→ ∠BAC = (180° - θ) .

therefore, we can conclude that, sum of angles made by same chord on major and minor segments is equal to 180° .

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