ABCD is a cyclic quadrilateral whose diagonal | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Since angles in the same segment of a circle are equal,we have $\angle BAC = \angle BDC$.Given $\angle BAC = 30^{\circ}$,therefore $\angle BDC = 3

Vedclass · Accepted Answer

$80^{\circ}; 50^{\circ}$

Vedclass · Answer

(A) Since angles in the same segment of a circle are equal,we have $\angle BAC = \angle BDC$.Given $\angle BAC = 30^{\circ}$,therefore $\angle BDC = 30^{\circ}$.In $\Delta BCD$,the sum of angles is $180^{\circ}$:$\angle BCD + \angle DBC + \angle BDC = 180^{\circ}$$\angle BCD + 70^{\circ} + 30^{\circ} = 180^{\circ}$$\angle BCD = 180^{\circ} - 100^{\circ} = 80^{\circ}$.Now,in $\Delta ABC$,since $AB = BC$,the angles opposite to equal sides are equal,so $\angle BCA = \angle BAC = 30^{\circ}$.Since $\angle BCD = \angle BCA + \angle ECD$,we have:$80^{\circ} = 30^{\circ} + \angle ECD$$\angle ECD = 80^{\circ} - 30^{\circ} = 50^{\circ}$.

$ABCD$ is a cyclic quadrilateral whose diagonals intersect at a point $E$. If $\angle DBC = 70^{\circ}$ and $\angle BAC = 30^{\circ}$,find $\angle BCD$. Further,if $AB = BC$,find $\angle ECD$.

Similar Questions

$A$ quadrilateral $ABCD$ is inscribed in a circle such that $AB$ is a diameter and $\angle ADC = 130^{\circ}$. Find $\angle BAC$.

$ABCD$ is a cyclic quadrilateral such that $AB$ is a diameter of the circle circumscribing it and $\angle ADC = 140^{\circ}$,then $\angle BAC$ is equal to (in $^{\circ}$)

If $BM$ and $CN$ are the perpendiculars drawn on the sides $AC$ and $AB$ of the triangle $ABC$,prove that the points $B, C, M$ and $N$ are concyclic.

In the figure,$ABCD$ is a cyclic quadrilateral in which $AC$ and $BD$ are its diagonals. If $\angle DBC = 55^{\circ}$ and $\angle BAC = 45^{\circ}$,find $\angle BCD$. (in $^{\circ}$)

$ABCD$ is a cyclic quadrilateral in which $\angle A = 80^{\circ}$ and $\angle B = 75^{\circ},$ then $\angle D = \dots$ (in $^{\circ}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module