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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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 | |||
From a point A, the length of a tangent to a circle is 8cm and distance of A from the circle is 10cm. The length of the diameter of the circle is | |||
| Right Option : A | |||
| View Explanation | |||
PT is a tangent to a circle whose centre is O. If PT = 12 cm and PO = 13 cm then find the radius of the circle. | |||
| Right Option : A | |||
| View Explanation | |||
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