Construction of Tangents to a Circle:
If a point lies on the circle, then there is only one tangent to the circle at this point and it is perpendicular to the radius through this point. Therefore, if you want to draw a tangent at a point of a circle, simply draw the radius through this point and draw a line perpendicular to this
radius through this point and this will be the required tangent at the point.
We are given a circle with center O and a point P outside it. We have to construct
the two tangents from P to the circle.
Steps of Construction:
1. Join PO and bisect it. Let M be the midpoint of PO.
2. Taking M as center and MO as radius, draw a circle. Let it intersect the given circle at the points Q and R.
3. Join PQ and PR. Then PQ and PR are the required two tangents , now let us see how this construction works. Join OQ. Then ∠ PQO is an angle in the semicircle and, therefore,∠ PQO = 90° Can we say that PQ ⊥ OQ? Since, OQ is a radius of the given circle, PQ has to be a tangent to the circle. Similarly, PR is also a tangent to the circle.
If a point lies on the circle, then there is only one tangent to the circle at this point and it is perpendicular to the radius through this point. Therefore, if you want to draw a tangent at a point of a circle, simply draw the radius through this point and draw a line perpendicular to this
radius through this point and this will be the required tangent at the point.
We are given a circle with center O and a point P outside it. We have to construct
the two tangents from P to the circle.
Steps of Construction:
1. Join PO and bisect it. Let M be the midpoint of PO.
2. Taking M as center and MO as radius, draw a circle. Let it intersect the given circle at the points Q and R.
3. Join PQ and PR. Then PQ and PR are the required two tangents , now let us see how this construction works. Join OQ. Then ∠ PQO is an angle in the semicircle and, therefore,∠ PQO = 90° Can we say that PQ ⊥ OQ? Since, OQ is a radius of the given circle, PQ has to be a tangent to the circle. Similarly, PR is also a tangent to the circle.
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