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    prove that the perpendicular at the point of contact to a tangent to a circle

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    Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.

    Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.

    Byju's Answer Standard X Mathematics

    Tangent Perpendicular to Radius at Point of Contact

    Prove that th... Question

    Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.

    Open in App Solution

    STEP :Proof

    Let us assume a circle with centre

    O and let AB

    be the tangent intersecting the circle at point

    P .

    Also let us assume a point

    X such that XP is perpendicular to AB .

    STEP 2 : Proving that

    XP

    passes through centre

    O We know that

    Tangent of a circle is perpendicular to radius at point of contact

    ⇒OP⊥AB

    (Tangent at any point of circle is perpendicular to the radius through point of contact)

    So, ∠OPB=90° ...(1)

    we have already assumed that

    XP is perpendicular to AB ∠XPB=90° ...(2) Now from equation (1) and (2) ∠OPB=∠XPB=90°

    This condition is possible only if line

    XP passes through O . Since, XP

    passes through centre

    O .

    Therefore, it is proved that the perpendicular at the point of contact to the tangent of a circle passes through the centre.

    Suggest Corrections 42

    SIMILAR QUESTIONS

    Q.

    Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.

    Q.

    State true or false:

    For a tangent, the perpendicular line from the point of contact to the circle passes through the centre.

    Q. Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contactQ. Prove that tangent drawn at any point of a circle is perpendicular to the radius through the point of contact.Q. Question 5

    Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.

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    स्रोत : byjus.com

    Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre of the circle.

    Click here👆to get an answer to your question ✍️ Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre of the circle.

    Question

    Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre of the circle.

    Medium Open in App Solution Verified by Toppr

    Given a circle with center O and AB the tangent intersecting circle at point P

    and prove that OP⊥AB

    We know that tangent of the circle is perpendicular to radius at points of contact Hence

    OP⊥AB So, ∠OPB=90 o ..........(i)

    Now lets assume some point X

    Such that XP⊥AN Hence ∠XPB=90 o .........(ii) From eq (i) & (ii) ∠OPB=∠XPB=90 o

    Which is possible only if line XP passes though O

    Hence perpendicular to tangent passes though centre

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    Ex 10.2, 5

    Ex 10.2,5 Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre. Given: Let us assume a circle with centre O & AB be the tangent intersecting circle at point P To prove: OP AB Proof: We know that Tangent of circle is perpendicular t

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    Ex 10.2, 5 - Chapter 10 Class 10 Circles (Term 2)

    Last updated at Aug. 5, 2021 by Teachoo

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    Transcript

    Ex 10.2,5 Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre. Given: Let us assume a circle with centre O & AB be the tangent intersecting circle at point P To prove: OP AB Proof: We know that Tangent of circle is perpendicular to radius at point of contact Hence, OP AB So, OPB = 90 Now lets assume some point X , such that XP AB Hence, XPB = 90 From (1) and (2) OPB = XPB = 90 Which is possible only if line XP passes through O Hence , perpendicular to tangent passes through centre

    Next: Ex 10.2, 6 →

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