Case Based Questions Test: Circles
15 Questions MCQ Test Mathematics (Maths) Class 10 | Case Based Questions Test: Circles
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Read the following text and answer the following question on the basis of the same:
A farmer has a field in the shape of triangle with AB = 13 cm, BC = 14 cm and AE = 7 cm. He wants to leave a space in the form of a circular field for growing wheat and the remaining for growing vegetables.
Q. The measure of BF is:
∴ AB = 13 cm (given)
∴ BF = AB – AF
= (13 – 7) cm
AE = 7 cm (given)
Then, AF = AE (Tangents of the circle)
⇒ AF = 7 cm.
[Proved, AF = 7 cm]
BF = 6 cm
Read the following text and answer the following question on the basis of the same:
A farmer has a field in the shape of triangle with AB = 13 cm, BC = 14 cm and AE = 7 cm. He wants to leave a space in the form of a circular field for growing wheat and the remaining for growing vegetables.
Q. The measure of CE + CD is:
∴ AB = 13 cm (given)
∴ BF = AB – AF
BC = 14 cm (given)
= (13 – 7) cm
AE = 7 cm (given)
Then, AF = AE (Tangents of the circle)
⇒ AF = 7 cm.
[Proved, AF = 7 cm]
BF = 6 cm
BF = 6 cm (Proved)
∴ BD = BF (Tangents of the circle)
So, BD = 6 cm.
and BD = 6 cm [Proved]
then CD = BC – BD
= (14 – 6) cm = 8 cm
but CD = CE (Tangents of the circle)
∴ CE = 8 cm
So, CD + CE = (8 + 8) cm = 16 cm.
Read the following text and answer the following question on the basis of the same:
A farmer has a field in the shape of triangle with AB = 13 cm, BC = 14 cm and AE = 7 cm. He wants to leave a space in the form of a circular field for growing wheat and the remaining for growing vegetables.
Q. The measure of AF is:
Then, AF = AE (Tangents of the circle)
⇒ AF = 7 cm.
Read the following text and answer the following question on the basis of the same:
A farmer has a field in the shape of triangle with AB = 13 cm, BC = 14 cm and AE = 7 cm. He wants to leave a space in the form of a circular field for growing wheat and the remaining for growing vegetables.
Q. The measure of BD is:
∴ AB = 13 cm (given)
BF = AB – AF
= (13 – 7) cm
[Proved in Q. 1., AF = 7 cm]
BF = 6 cm
BF = 6 cm (Proved)
∴ BD = BF (Tangents of the circle)
So, BD = 6 cm.
Read the following text and answer the following question on the basis of the same:
A farmer has a field in the shape of triangle with AB = 13 cm, BC = 14 cm and AE = 7 cm. He wants to leave a space in the form of a circular field for growing wheat and the remaining for growing vegetables.
Q. The measure of AC is:
∴ AB = 13 cm (given)
BF = AB – AF
= (13 – 7) cm
AE = 7 cm (given)
Then, AF = AE (Tangents of the circle)
⇒ AF = 7 cm.
[Proved AF = 7 cm]
BF = 6 cm
BC = 14 cm (given)
and BD = 6 cm [Proved in Q. 3]
then CD = BC – BD
= (14 – 6) cm = 8 cm
but CD = CE (Tangents of the circle)
∴ CE = 8 cm
So, CD + CE = (8 + 8) cm = 16 cm.
CE = 8 cm
and AE = 7 cm (given)
then, AC = AE + EC
= (7 + 8) cm
= 15 cm.
Both Assertion and Reason are true but Reason is not correct explanation of Assertion
In the following figure, a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC, AB, AD and CD at points P, Q, R and S respectively. If AB = 29 cm, AD = 23 cm, ∠B = 90° and DS = 5 cm.
Q. Find the value of AR:
Here, AD = 23 cm (given)
and
Here, DS = 5 cm
but DR = DS (Length of tangents are equal)
then DR = 5 cm.
DR = 5 cm (Proved)
then AR = AD – DR cm
= (23 – 5) cm = 18 cm.
Both Assertion and Reason are true but Reason is not correct explanation of Assertion
In the following figure, a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC, AB, AD and CD at points P, Q, R and S respectively. If AB = 29 cm, AD = 23 cm, ∠B = 90° and DS = 5 cm.
Q. Find the value of BP:
AB = 29 cm (given) but AQ = AR(Length of tangents are equal) then AQ = 18 cm
Here, AD = 23 cm (given)
and
Here, DS = 5 cm
but DR = DS (Length of tangents are equal)
then DR = 5 cm.
DR = 5 cm (Proved)
then AR = AD – DR cm
= (23 – 5) cm = 18 cm. [Proved]
∴ BQ = AB – AQ
= (29 – 18) cm = 11 cm.
BQ = 11 cm [Proved]
and BP = BQ (Length of tangents are equal)
∴ BP = 11 cm.
Both Assertion and Reason are true but Reason is not correct explanation of Assertion
In the following figure, a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC, AB, AD and CD at points P, Q, R and S respectively. If AB = 29 cm, AD = 23 cm, ∠B = 90° and DS = 5 cm.
Q. Find the value of DR:
but DR = DS
(Length of tangents are equal)
then DR = 5 cm.
Both Assertion and Reason are true but Reason is not correct explanation of Assertion
In the following figure, a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC, AB, AD and CD at points P, Q, R and S respectively. If AB = 29 cm, AD = 23 cm, ∠B = 90° and DS = 5 cm.
Q. Find the value of QB:
AB = 29 cm (given)
but AQ = AR (Length of tangents are equal)
then AQ = 18 cm
Here, AD = 23 cm (given)
and
Here, DS = 5 cm
but DR = DS (Length of tangents are equal)
then DR = 5 cm.
DR = 5 cm (Proved)
then AR = AD – DR cm
= (23 – 5) cm = 18 cm. [Proved]
∴ BQ = AB – AQ
= (29 – 18) cm = 11 cm.
Both Assertion and Reason are true but Reason is not correct explanation of Assertion
In the following figure, a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC, AB, AD and CD at points P, Q, R and S respectively. If AB = 29 cm, AD = 23 cm, ∠B = 90° and DS = 5 cm.
Q. AR is equal to:
Read the following text and answer the following questions on the basis of same: A ferris wheel (Or a big wheel in the United Kingdom) is an amusement ride consisting of a rotating upright wheel with multiple passenger carrying components attached to the rim in such a way that as the wheel turns, they are kept upright, usually by gravity.
After taking a ride in Ferris wheel Aarti came out from the crowd and was observing her friends who were enjoying the ride. She was curios about the different angles and measures that wheel will form. She forms the figure as given below:
Q. Find ∠RQP
∠RSQ =∠RQP = 75°
[Angles in alternate segment]
Read the following text and answer the following questions on the basis of same: A ferris wheel (Or a big wheel in the United Kingdom) is an amusement ride consisting of a rotating upright wheel with multiple passenger carrying components attached to the rim in such a way that as the wheel turns, they are kept upright, usually by gravity.
After taking a ride in Ferris wheel Aarti came out from the crowd and was observing her friends who were enjoying the ride. She was curios about the different angles and measures that wheel will form. She forms the figure as given below:
Q. Find ∠ORP
Read the following text and answer the following questions on the basis of same: A ferris wheel (Or a big wheel in the United Kingdom) is an amusement ride consisting of a rotating upright wheel with multiple passenger carrying components attached to the rim in such a way that as the wheel turns, they are kept upright, usually by gravity.
After taking a ride in Ferris wheel Aarti came out from the crowd and was observing her friends who were enjoying the ride. She was curios about the different angles and measures that wheel will form. She forms the figure as given below:
Q. In the given figure, Find ∠ROQ
∠ROQ + 30° = 180°
∠ROQ = 150°
Read the following text and answer the following questions on the basis of same: A ferris wheel (Or a big wheel in the United Kingdom) is an amusement ride consisting of a rotating upright wheel with multiple passenger carrying components attached to the rim in such a way that as the wheel turns, they are kept upright, usually by gravity.
After taking a ride in Ferris wheel Aarti came out from the crowd and was observing her friends who were enjoying the ride. She was curios about the different angles and measures that wheel will form. She forms the figure as given below:
Q. Find ∠RSQ
Read the following text and answer the following questions on the basis of same: A ferris wheel (Or a big wheel in the United Kingdom) is an amusement ride consisting of a rotating upright wheel with multiple passenger carrying components attached to the rim in such a way that as the wheel turns, they are kept upright, usually by gravity.
After taking a ride in Ferris wheel Aarti came out from the crowd and was observing her friends who were enjoying the ride. She was curios about the different angles and measures that wheel will form. She forms the figure as given below:
Q. Find ∠ORQ
∠ORQ + ∠OQR + ∠ROQ= 180°
2∠ORQ = 180° – ∠ROQ
2∠ORQ = 180° – 150° = 30°
∠ORQ = 15°
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