Math, asked by SᴘᴀʀᴋʟɪɴɢCᴀɴᴅʏ, 9 months ago

Give all the theorem of circle of class 10​

Answers

Answered by ItzMADARA
19

Theorem 1

The tangent at any point of a circle is perpendicular to the radius through the point of contact.

Construction: Draw a circle with centre O. Draw a tangent XY which touches point P at the circle.

10 circle of theorem 1

To Prove: OP is perpendicular to XY.

Draw a point Q on XY; other than O and join OQ. Here OQ is longer than the radius OP.

OQ > OP

For every point on the line XY other than O, like Q1, Q2, Q3, ……….Qn;

OQ1>OP

OQ2>OP

OQ3>OP

OQ4>OP

Since OP is the shortest line

Hence, OP ⊥ XY proved

10 Mathsexcellup logo

Circle

Theorems on Circle

Tangent to a circle: A line which intersects a circle at any one point is called the tangent.

There is only one tangent at a point of the circle.

The tangent to a circle is perpendicular to the radius through the point of contact.

The lengths of the two tangents from an external point to a circle are equal.

Theorem 2

The lengths of tangents drawn from an external point to a circle are equal.

Construction: Draw a circle with centre O. From a point P outside the circle, draw two tangents P and R.

10 circle theorem 1

To Prove: PQ = PR

Proof: In Δ POQ and Δ POR

O

Q

=

O

R

(radii)

P

O

=

P

O

(common side)

P

Q

O

=

P

R

O

(Right angle)

Hence;

Δ

P

O

Q

Δ

P

O

R

proved

hope it helps you.....

Good night Dear......

Answered by SmudgeJasmine
9

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  • First circle theorem - angles at the centre and at the circumference.
  • Second circle theorem - angle in a semicircle.
  • Third circle theorem - angles in the same segment.
  • Fourth circle theorem - angles in a cyclic quadlateral.
  • Fifth circle theorem - length of tangents.
  • Sixth circle theorem - angle between circle tangent and radius.
  • Seventh circle theorem - alternate segment theorem.
  • Eighth circle theorem - perpendicular from the centre bisects the chord

HOPE THIS HELPS YOU DEAR

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