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Mathematics > UNIT IV: Geometry > Learn Circles

Circles

Circles relates to CBSE - Class 10/Mathematics/UNIT IV: Geometry

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Class-9-Maths L-9 Circles Ex 9.3 Q2

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Answered on 16/04/2024 Learn CBSE - Class 10/Mathematics/UNIT IV: Geometry/Circles

2. Prove that the parallelogram circumscribing a circle is a rhombus.

Sadika

To prove that the parallelogram circumscribing a circle is a rhombus, we first need to establish some properties: In a parallelogram, opposite sides are equal in length. In a parallelogram, opposite angles are equal in measure. Now, let's consider a parallelogram ABCD circumscribing a circle with center... read more

To prove that the parallelogram circumscribing a circle is a rhombus, we first need to establish some properties:

  1. In a parallelogram, opposite sides are equal in length.
  2. In a parallelogram, opposite angles are equal in measure.

Now, let's consider a parallelogram ABCD circumscribing a circle with center O. Let P, Q, R, and S be the points of tangency between the circle and the sides of the parallelogram, as shown below:
        P-----Q
       /       \
      /         \
     A-----------B
     |     O     |
     |           |
     D-----------C
      \         /
       \       /
        R-----S

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Answered on 16/04/2024 Learn CBSE - Class 10/Mathematics/UNIT IV: Geometry/Circles

3. In a right triangle ABC in which ∠B = 90°, a circle is drawn with AB as diameter intersecting the...
3. In a right triangle ABC in which ∠B = 90°, a circle is drawn with AB as diameter intersecting the hypotenuse AC and P. Prove that the tangent to the circle at P bisects BC.

Sadika

Let's denote the midpoint of BC as M. To prove that the tangent to the circle at P bisects BC we need to show that BM=MC. read more

Let's denote the midpoint of BC as M. To prove that the tangent to the circle at P bisects BC we need to show that BM=MC.

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Answered on 16/04/2024 Learn CBSE - Class 10/Mathematics/UNIT IV: Geometry/Circles

5. Prove that the line segment joining the point of contact of two parallel tangents of a circle passes...
5. Prove that the line segment joining the point of contact of two parallel tangents of a circle passes through its centre.

Sadika

Let's denote the center of the circle as O, and the points of contact of the two parallel tangents as P and Q. The two tangents are parallel, so OP and OQ are parallel as well. read more

Let's denote the center of the circle as O, and the points of contact of the two parallel tangents as P and Q. The two tangents are parallel, so OP and OQ are parallel as well.

 

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Answered on 16/04/2024 Learn CBSE - Class 10/Mathematics/UNIT IV: Geometry/Circles

6. If from an external point P of a circle with centre O, two tangents PQ and PR are drawn such that...
6. If from an external point P of a circle with centre O, two tangents PQ and PR are drawn such that ∠QPR = 120°, prove that 2PQ = PO.

Sadika

In the given scenario, let's denote: read more

In the given scenario, let's denote:

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Answered on 16/04/2024 Learn CBSE - Class 10/Mathematics/UNIT IV: Geometry/Circles

7. If the angle between two tangents drawn from an external point P to a circle of radius a and centre...
7. If the angle between two tangents drawn from an external point P to a circle of radius a and centre O are 60°, then find the length of OP.

Sadika

Let's denote:::: the above question read more

Let's denote:::: the above question

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