Consider a circle with centre at C. Let OP, OQ denote respectively the tangents to the circle drawn from a point O outside the circle. Let R be a point on OP and S be a point on OQ such that OR × SQ = OS × RP. Which of the following statement(s) is/are correct (1) If X is the circle with centre at O and radius OR, and Y is the circle with centre at O and radius OS, then X = Y (2) ∠POC + ∠QCO = 90° Select the correct answer using the code given below.?

1 only
2 only
Both 1 and 2
Neither 1 nor 2

LohaHridoy

6 views

2025-01-04 04:42

1 Answers

AhmedNazir

Option 3 : Both 1 and 2

⇒ RP = SQ

⇒ OP – RP = OS – SQ

⇒ OR = OS

Statement I:

Both X and Y are circles with same centre and radius

⇒ X = Y

⇒ Statement I is true

In quadrilateral OPCQ

⇒ ∠O + ∠P + ∠Q + ∠C = 360°

⇒ 2∠POC + 90° + 90° + 2∠QCO = 360

⇒ 2∠POC + 2∠QCO = 180°

⇒ ∠POC + ∠QCO = 90°

⇒ Statement II is true

∴ Both I and II are true.

6 views Answered 2022-09-04 04:29

Related Questions

Two tangents EA and EB are drawn on a circle from a point E which is outside the circle of center O. If ∠AEB = 80°, find the value of ∠AOB.?

1 Answers 4 Views

A tangent is drawn from a point p outside the circle, which touches the circle at point A and B, another tangent is drawn from a point E on the circumference on the circle, which touches the line PA and PB at C and D, if PC measures 8 cm, PD measures 9 cm and CD measures 7 cm, then find the radius of circle.?

1 Answers 5 Views

ST is the diameter of a circle with centre O. Two tangents AB and CD are drawn at to the circle which touches the circle at point S and T respectively. If one more tangent EF is drawn to the circle which cuts tangents AB and CD at point P & Q respectively, then find the value of ∠POQ.?

1 Answers 4 Views

Choose the CORRECT option about the two tangents drawn to the circle from the external point (1) The tangents subtend equal angles at the centre of the circle. (2) The tangents drawn from the external point to a circle are equal in length. (3) The tangents are equally inclined to the segment which joins the centre to that point.?

1 Answers 4 Views

A = Area of the largest circle drawn inside a square of side 1 cm. B = Sum of areas of 4 identical (largest possible) circles drawn inside a square of side 1 cm. C = Sum of areas of 9 identical circle (largest possible) drawn inside a square of side 1 cm. D = Sum of area of 16 identical circles (largest possible) drawn inside a square of side 1 cm. Which of the following is TRUE about A, B, C and D?

1 Answers 5 Views

One Statement is given followed by two Assumptions, I and II. You have to consider the statement to be true, even if it seems to be at variance from commonly known facts. You are to decide which of the given assumptions can definitely be drawn from the given statement. Indicate your answer. Statement: All the employees are unsatisfied with the organization. Assumption I: The organization does not value the employees and does not give them perks. Assumption II: Employees are mean and greedy and are looking for ways to switch to another organization.?

1 Answers 5 Views

Consider a circle with centre at O and radius 7 cm. Let QR be the chord of length 2 cm and let P be the midpoint of QR. Let CD be another chord of this circle passing through P such that ∠CPQ is acute. If M is the midpoint of CD and MP = √24 cm, then which of the following statements are correct (1) ∠QPD = 135° (2) If CP = m cm and PD = n cm, then m and n are the roots of the quadratic equation x2 – 10x + 1 = 0 (3) The ratio of triangle OPR to the area of triangle OMP is 1 ∶ 2√2 Select the correct answer using the code given below.?

1 Answers 7 Views

In the following question, a statement is given followed by two conclusions numbered I and II. You have to consider the statement to be true, even if it seems to be at variance from commonly known facts. You are to decide which of the given conclusions can be drawn definitely from the given statement and indicate your answer accordingly. Statement: Teachers should attend the workshop. Conclusion: I. Because they get updated with new things. II. Their time gets wasted in this.?

1 Answers 5 Views

One Statement is given followed by two Assumptions, I and II. You have to consider the statement to be true, even if it seems to be at variance with commonly known facts. You are to decide which of the given assumptions can definitely be drawn from the given statement. Indicate your answer. Statement: All the employees are unsatisfied with the organization. Assumption I: The organization does not value the employees and does not give them perks. Assumption II: Employees are mean and greedy and are looking for ways to switch to another organization.?

1 Answers 5 Views

A statement is given followed by two inferences I and II. You have to consider the statement to be true even if it seems to be at variance from commonly known facts. You have to decide which of the given inferences, if any, follow from the given statement Statement: U.S. President Donald Trump signed an order on Tuesday to keep open the military detention centre at Guantanamo Bay after his Democratic predecessor, Barack Obama, tried unsuccessfully to close the prison that has drawn international condemnation. Inferences: Guantanamo Bay Detention Centre was never closed during the reign of President Barack Obama. Guantanamo Bay Detention Centre would increase the capacity to accommodate detainees.?

1 Answers 5 Views

এক্সাম দিয়ে মেধা যাচাই করুন

Job Preparation (1125)

Admission (754)

এসএসসি (10)

এইচএসসি (5)