Question

Three points A,B and C are vertices of cyclic quadrilateral such that ∟A = 900

,

AB =4cm and AC =3cm then draw a circle which passes through these three

points and also find the fourth vertex and area of circle.

(i) Draw neatly

(ii) Write steps of construction
ITS IMPORTENT NOW ANY

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Answer 1

Given :- Three points A,B and C are vertices of cyclic quadrilateral such that ∟A = 90°, AB = 4cm and AC =3cm .

Answer :-

given that,

→ ∠CAB = 90°

so,

→ CB = Diameter of the circle. { Angle in a semi - circle is equal to 90°. }

then, in Right angled ∆CAB ,

→ CB = √(CA² + AB²) { By pythagoras theorem.}

→ CB = √(3² + 4²)

→ CB = √(9 + 16)

→ CB = √25

→ CB = 5 cm = Diameter of circle.

so,

→ Radius = Diameter / 2 = 2.5 cm .

therefore,

→ Area of circle = πr² = 3.14 * 2.5 * 2.5 = 19.625 cm².

now, Let fourth vertex is D.

so,

→ ∠CAB + ∠CDB = 180° { sum of opposite angles of a cyclic quadrilateral is equal to 180°.}

→ 90° + ∠CDB = 180°

→ ∠CDB = 180° - 90°

→ ∠CDB = 90° .

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