In the figure below (not drawn to scale), rectangle ABCD is inscribed in the circle with center at O. The length of side AB is greater than side BC. The ratio of the area of the circle to the area of the rectangle ABCD is $\pi : \sqrt{3}$. The line segment DE intersects AB at E such that $\angle \text{DOC} = \angle \text{ADE}$. The ratio $AE : AD$ is:
In the figure (not drawn to scale) given below, if $AD = CD = BC$ and $\angle DBC = 96^\circ$, how much is the value of $\angle DBC$?
In the figure (not drawn to scale) given below, P is a point on AB such that $AP : PB = 4 : 3$. PQ is parallel to AC and QD is parallel to CP. In $\triangle ARC$, $\angle ARC = 90^\circ$, and in $\triangle PQS$, $\angle PQS = 90^\circ$. The length of QS is 6 cm. What is the ratio of $AP : PD$?
In the above figure, ACB is a right-angled triangle. CD is the altitude. Circles are inscribed within the triangles \( \triangle ACD \) and \( \triangle ABC \). P and Q are the centres of the circles. The distance PQ is
Aboy is asked to put one mango in a basket when ordered ’One’, one orange when ordered ’Two’, one apple when ordered ’Three’, and is asked to take out from the basket one mango and an orange when ordered ’Four’. A sequence of orders is given as:1 2332142314223314113234
Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters.
In the diagram,\[ \angle ABC = 90^\circ = \angle DCH = \angle DOE = \angle EHK = \angle FKL = \angle GLM = \angle LMN \]\[ AB = BC = 2CH = 2CD = EH = FK = 2HK = 4KL = 2LM = MN \]
