CBSE Class 10 Answered
To Prove: OP is perpendicular to AB.
Construction: Take any point Q, other than P, on the tangent AB. Join OQ.
Since, Q is a point on the tangent AB, other than the point of contact P, so Q will be outside the circle.
Let OQ intersect the circle at R.
Then, OQ=OR+RQ
OQ>OR
OQ>OP (OR=OP=radius)
Thus, OP
But, among all the line segments, joining the point O to a point on AB, the shortest one is the perpendicular from O on AB.
Hence, OP is perpendicular to AB.
Given: A circle C (O, r) and a tangent AB at a point P.
To Prove: OP is perpendicular to AB.
Construction: Take any point Q, other than P, on the tangent AB. Join OQ.
Since, Q is a point on the tangent AB, other than the point of contact P, so Q will be outside the circle.
Let OQ intersect the circle at R.
Then, OQ=OR+RQ
OQ>OR
OQ>OP (OR=OP=radius)
Thus, OP
But, among all the line segments, joining the point O to a point on AB, the shortest one is the perpendicular from O on AB.
Hence, OP is perpendicular to AB.Gi