• +91 9971497814
• info@interviewmaterial.com

# RD Chapter 16- Circles Ex-16.5 Interview Questions Answers

### Related Subjects

Question 1 : In the given figure, ΔABC is an equilateral triangle. Find m∠BEC.

It is given that,   is an equilateral triangle

We have to find
Since   is an equilateral triangle.
So
And
…… (1)
Since, quadrilateral BACE  is a cyclic qualdrilateral

So ,                                          (Sum of opposite angles of cyclic quadrilateral is .)

Hence

Question 2 : In the given figure, ΔPQR is an isosceles triangle with PQ = PR and m ∠PQR = 35°. Find m ∠QSR and m ∠QTR.

Disclaimer: Figure given in the book was showing m∠PQR as m∠SQR.
It is given that ΔPQR is an isosceles triangle with PQ = PR and m∠PQR = 35°
We have to find the m∠QSR and m∠QTR
Since ΔPQR is an isosceles triangle
So ∠PQR = ∠PRQ = 35°
Then

Since PQTR is a cyclic quadrilateral
So
In cyclic quadrilateral QSRT we have

Hence,
and

Question 3 : In the given figure, O is the centre of the circle. If ∠BOD = 160°, find the values of x and y.

It is given that O is centre of the circle and ∠BOD = 160°

We have to find the values of x and y.
As we know that the angle subtended by an arc of a circle at the centre is double the angle subtended by it at any point on the remaining part of the circle.
Therefore,

So,
x + y = 180°              (Sum of opposite angles of a cyclic quadrilateral is 180°.)

Hence  and

Question 4 : In the given figure, ABCD is a cyclic quadrilateral. If ∠BCD = 100° and ∠ABD = 70°, find ∠ADB.

It is given that ∠BCD = 100° and ∠ABD = 70°

We have to find the ∠ADB
We have
∠A + ∠C = 180°                     (Opposite pair of angle of cyclic quadrilateral)
So,
Now in   is   and
Therefore,

Hence,

Question 5 : If ABCD is a cyclic quadrilateral in which AD || BC (In the given figure). Prove that ∠B = ∠C.

It is given that, ABCD is cyclic quadrilateral in which AD || BC

We have to prove
Since, ABCD is a cyclic quadrilateral
So,
and                ..… (1)
and                (Sum of pair of consecutive interior angles is 180°) …… (2)
From equation (1) and (2) we have
…… (3)
…… (4)
Hence Proved

Question 6 : In the given figure, O is the centre of the circle. Find ∠CBD.

It is given that,

We have to find
Since,      (Given)
So,
(The angle subtended by an arc of a circle at the centre is double the angle subtended by it at any point on the remaining part of the circle.)

Now,

(Opposite pair of angle of cyclic quadrilateral)
So,

…… (1)
(Linear pair)
( )

Hence

Question 7 : In the given figure, AB and CD are diameters of a circle with centre O. If ∠OBD = 50°, find ∠AOC.

It is given that, AB and CD are diameter with center O and

We have to find
Construction: Join the point A and D to form line AD
Clearly arc AD subtends   at B and   at the centre.
Therefore,  ∠AOD=2∠ABD=100°∠AOD=2∠ABD=100° …… (1)
Since CD is a straight line then

∠DOA+∠AOC=180°        (Linear pair)∠DOA+∠AOC=180°        Linear pair

Hence

Question 8 : On a semi-circle with AB as diameter, a point C is taken, so that m (∠CAB) = 30°. Find m (∠ACB) and m (∠ABC).

It is given that,   as diameter,   is centre and

We have to find   and
Since angle in a semi-circle is a right angle therefore

In   we have
(Given)
(Angle in semi-circle is right angle)
Now in   we have

Hence  and

Question 9 : In a cyclic quadrilateral ABCD if AB || CD and ∠B = 70°, find the remaining angles.

It is given that, ABCD is a cyclic quadrilateral such that AB || CD and

Sum of pair of opposite angles of cyclic quadrilateral is 180°.
(  given)
So,
Also AB || CD and BC transversal
So,

Now

Question 10 : In a cyclic quadrilateral ABCD, if m ∠A = 3 (m ∠C). Find m ∠A.

It is given that