Question
ABC is a triangle in which AB = AC. Points D and E are points on the side AB and AC respectively such that AD = AE. Show that the points B, C, E and D lie on a same circle
✓
Answer
∠B = ∠C ...(Given AB = AC)
AD + DB = AE + EC
BD = EC ...(Given AD = AE)
DE parallel BC Since AEC is a straight line.
∠AED + ∠CED = 180°
∠CBD + ∠CED = 180°
Similarly of the opposite angles = 180°
∴ BCED is a cyclic quadrilateral
AD + DB = AE + EC
BD = EC ...(Given AD = AE)
DE parallel BC Since AEC is a straight line.
∠AED + ∠CED = 180°
∠CBD + ∠CED = 180°
Similarly of the opposite angles = 180°
∴ BCED is a cyclic quadrilateral
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Find the excluded values, of the following expression
$
\frac{x^3-27}{x^3+x^2-6 x}
$
→$
\frac{x^3-27}{x^3+x^2-6 x}
$
If $x \sin ^3 \theta+y \cos ^3 \theta=\sin \theta \cos \theta$ and $x \sin \theta=y \cos \theta$, then prove that $x^2+y^2=1$
→The function ' $t$ ' which map temperature in Celsius $( C )$ into temperature in Fahrenheit $( F )$ is defined by $t(C)=F$ where $F=\frac{9}{5} C+32$. Find, $t(0)$
→The ratio of the radii of two right circular cones of the same height is 1 : 3. Find the ratio of their curved surface area when the height cone is 3 times the radius of the smaller cone.
The function ' $t$ ' which map temperature in Celsius $(C)$ into temperature in Fahrenheit $(F)$ is defined by $t(C)=F$ where $F=\frac{9}{5} C+32$. Find, $t(-10)$
→Find the area of triangle AGF
If the mean and coefficient of variation of a data are 15 and 48 respectively, then find the value of standard deviation.
Find the sum of the following
$3, 7, 11, …$ up to $40$ terms
→$3, 7, 11, …$ up to $40$ terms
If A is of order p × q and B is of order q × r what is the order of AB and BA?
Two unbiased dice are rolled once. Find the probability of getting the sum as a prime number