Answer
Verified
400.2k+ views
Hint: If A, B, C and D are concyclic then these points are passing through a circle. Now, draw a circle passing through these points and it is given that $\angle BAC={{45}^{0}}$ so $\angle BDC$ will be found out by the property that the points on the circle which are lying on the same side of the given chord are subtending equal angles on that chord.
Complete step-by-step answer:
It is given that A, B, C and D are concyclic so we can draw a circle passing through these points.
In the above diagram, A, B, C and D are lying on the circle and $\angle BAC={{45}^{0}}$.
We have to find $\angle BDC$. As you can see that $\angle BDC\And \angle BAC$ lie on the same side of the chord BC so we can use the property that which says that if A, B, C and D are concyclic and points A and D lie on the same side of the chord (or side) BC then angle subtended by the points lying on the same side of the side are equal.
As $\angle BDC\And \angle BAC$ lie on the same side of the chord BC so using the property of concyclic points that we have just discussed we can say that both the angles are equal.
So, $\angle BDC=\angle BAC={{45}^{0}}$.
Hence, the correct option is (a).
Note: If you don’t know the property of concyclic points. In the greed of getting more marks don’t try to consider the $\angle B\And \angle C$ as ${{90}^{0}}$ and then try to get the value of $\angle BDC$. You might think if you assume these angles as ${{90}^{0}}$ you will somehow get the answer. Don’t do such adventures in the exam, you might take the risk, if the question has no negative marking. Moreover it is advisable to know what concyclic points mean.
Complete step-by-step answer:
It is given that A, B, C and D are concyclic so we can draw a circle passing through these points.
In the above diagram, A, B, C and D are lying on the circle and $\angle BAC={{45}^{0}}$.
We have to find $\angle BDC$. As you can see that $\angle BDC\And \angle BAC$ lie on the same side of the chord BC so we can use the property that which says that if A, B, C and D are concyclic and points A and D lie on the same side of the chord (or side) BC then angle subtended by the points lying on the same side of the side are equal.
As $\angle BDC\And \angle BAC$ lie on the same side of the chord BC so using the property of concyclic points that we have just discussed we can say that both the angles are equal.
So, $\angle BDC=\angle BAC={{45}^{0}}$.
Hence, the correct option is (a).
Note: If you don’t know the property of concyclic points. In the greed of getting more marks don’t try to consider the $\angle B\And \angle C$ as ${{90}^{0}}$ and then try to get the value of $\angle BDC$. You might think if you assume these angles as ${{90}^{0}}$ you will somehow get the answer. Don’t do such adventures in the exam, you might take the risk, if the question has no negative marking. Moreover it is advisable to know what concyclic points mean.
Recently Updated Pages
Assertion The resistivity of a semiconductor increases class 13 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE
Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE
What are the possible quantum number for the last outermost class 11 chemistry CBSE
Is C2 paramagnetic or diamagnetic class 11 chemistry CBSE
Trending doubts
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE
Select the correct plural noun from the given singular class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
The sum of three consecutive multiples of 11 is 363 class 7 maths CBSE
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
How many squares are there in a chess board A 1296 class 11 maths CBSE