Advertisements
Advertisements
Question
In a rectangle ABCD, AB = 25 cm and BC = 15. In what ratio does the bisector of ∠C divide AB?
Advertisements
Solution
Given, AB = 25 cm and BC = 15 cm
Now, In rectangle ABCD,
CO is the bisector of ∠C and it divides AB.
∴ ∠OCB = ∠OCD = 45°
∴ ∠OCB = ∠OCD = 45°
In ΔOCB, we have
∠CBO + ∠OCB + ∠COB = 180° ...[Angle sum property of triangle]
90° + 45° + ∠COB = 180°
∠COB = 180° – 90° + 45°
∠COB = 180° – 135° = 45°
Now, In ΔOCB,
∠OCB = ∠COB
Then, OB = OC
⇒ OB = 15 cm
CO divides AB in the ratio AO : OB
Let AO be x, then OB = AB – x = 25 – x
Hence, AO : OB = x : 25 – x
⇒ 10 : 15
⇒ 2 : 3
APPEARS IN
RELATED QUESTIONS
ABC is a right-angled triangle and O is the mid point of the side opposite to the right angle. Explain why O is equidistant from A, B and C. (The dotted lines are drawn additionally to help you)
The angle between the altitudes of a parallelogram, through the same vertex of an obtuse angle of the parallelogram is 60°. Find the angles of the parallelogram.
Which of the following statement is true for a rectangle?
It has all its sides of equal length.
Using opposite angles test for parallelogram, prove that every rectangle is a parallelogram.
Diagonals of a rectangle ABCD intersect at point O. If AC = 8 cm then find BO and if ∠CAD =35° then find ∠ACB.
State with Reason Whether the Following Statement is ‘True’ Or ‘False’.
Every rectangle is a parallelogram.
If the diagonals of a quadrilateral are equal and bisect each other, then the quadrilateral is a ______.
Every trapezium is a rectangle.
In rectangle PAIR, find ∠ARI, ∠RMI and ∠PMA.
A line l is parallel to line m and a transversal p intersects them at X, Y respectively. Bisectors of interior angles at X and Y interesct at P and Q. Is PXQY a rectangle? Given reason.
