In the figure, lines m and n are tangent lines to circle A. What can you say about quadrilateral ABCD? Explain.
Answers
Quadrilateral ABCD is a square
Step-by-step explanation:
Given that
m and n are tangents to the circle with centre at A
AD and AB will be the radius of the circle
Therefore, AD = AB
m is tangent to the circle at point D
Therefore, line joining D and the centre A i.e.e line AD will be perpendicular to m
Therefore, CD ⊥ AD
∴ ∠ADC = 90°
Similarly, CB ⊥ AB
∴ ∠ABC = 90°
It is shown in the figure that
∠BAD = 90°
And we know that sum of all the angles of a quadrilateral is 360°
∴ ∠BCD = 90°
Thus all the angles of quadrilateral ABCD are right angles and two adjacent sides are equal
Therefore, the quadrilateral ABCD is a square
Hope this answer is helpful.
Know More:
Q: In the figure, a circle is inscribed in a quadrilateral ABCD in which Angle B equal to 90°, AD = 23 cm AB =29 cm and DS = 5 cm. Find the radius of the circle.
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