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प्रश्न
Draw a circle of radius 3 cm. Take any point K on it. Draw a tangent to the circle from point K without using center of the circle.
उत्तर
Analysis:
As shown in the figure, line l is a tangent to the circle at point K.
seg BK is a chord of the circle and ∠BAK is an inscribed angle.
By tangent secant angle theorem,
∠BAK = ∠BKR
By converse of tangent secant angle theorem,
If we draw ∠BKR such that ∠BKR = ∠BAK, then ray KR
i.e. (line l) is a tangent at point K.
Steps of construction:
- Draw a circle of radius 3 cm and take any point K on it.
- Draw chord BK of any length and an inscribed ∠BAK of any measure.
- By taking A as a centre and any convenient distance on the compass draw an arc intersecting the arms of ∠BAK in points P and Q.
- With K as a centre and the same distance in the compass, draw an arc intersecting the chord BK at point S.
- Taking radius equal to PQ and S as the centre, draw an arc intersecting the previously drawn arc. Name the point of intersection as R.
- Draw line RK. Line RK is the required tangent to the circle.
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