Relationship Between Radius of Circle And Tangent
Relationship Between Radius of Circle And Tangent
Relationship between Radius of circle with tangent:
Theorem: The tangent at any point of a circle is perpendicular to the radius through the point of contact.
Given : A circle with center O. XY is a tangent and P is the point of contact. To Prove: OP is perpendicular to XY Construction: Take a point Q on XY join OQ. Proof: Now point Q lies outside the circle because the tangent just touches the circle at point P So as Q points lies on XY therefore it is outside the circle. OQ > radius of the circle [ Q is outside the circle] OQ > OP So any point on XY the distance from the center will be more than radius That is OP is the shortest of all the distances of the point O to the points on XY. So, OP is perpendicular to XY [ because the shortest distance is perpendicular] |  I |
Illustration: A point P is 13 cm from the centre of the circle. The length of the tangent from P to the circle is 12 cm. Find the radius of the circle.
Solution Since the tangent to a circle is perpendicular to the radius through the point of contact, It is given that OP = 13 cm, PT = 12 cm and let OT = r cm In right triangle OTP,
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PQ is a tangent drawn from a point P to a circle with centre O and QOR is a diameter of the circle such that ∠POR=120°, then ∠OPQ is | |||
| Right Option : C | |||
| View Explanation | |||
The length of the tangent drawn from a point 8 cm away from the centre of a circle, of radius 6 cm, is _______________ | |||
| Right Option : C | |||
| View Explanation | |||
In the given figure, O is the centre of a circle, PQ is a chord and PT is the tangent at P. If ∠POQ = 70, then ∠TPQ is equal to ______________ | |||
| Right Option : B | |||
| View Explanation | |||
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