Advertisements
Advertisements
प्रश्न
If the sides of a rectangle touch a circle, prove that the rectangle is a square.
बेरीज
Advertisements
उत्तर
A rectangle with all sides touching a circle implies the circle is an incircle.
To Prove
A rectangle whose four sides touch a circle is a square.
A rectangle with all sides touching a circle implies that the circle is an incircle of the rectangle.
Let the rectangle be ABCD, with length l and breadth b.
A circle touches all four sides at points P, Q, R, and S.
In any quadrilateral that has an incircle,
the sum of the lengths of opposite sides is equal:
AB + CD = BC + AD.
For rectangle ABCD:
AB = CD = l,
BC = AD = b.
l + l =b + b
2l = 2b
l = b
Since the length and breadth are equal, the rectangle is a square.
AB = CD = l
shaalaa.com
या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
