Draw a circle with the help of a bangle. Take a point outside the circle. Construct the pair of tangents from this point to the circle.
Solution:
Steps of construction:
Draw any circle using a bangle.
To find its centre:
- Draw two chords on the circle say AB and CD.
- Draw the perpendicular bisectors of AB and CD to intersect at O.
Now, ‘O’ is the centre of the circle (since the perpendiculars drawn from the centre of a circle to any chord bisect the chord and vice versa).
To draw the tangents from a point ‘P’ outside the circle:
- Take a point P outside the circle and draw the perpendicular bisector of OP which meets at OP at O’.
- With O’ as the centre and OO’ as radius draw a circle that cuts the given circle at Q and R.
- Join PQ and PR.
Thus, PQ and PR are the required tangents.
Proof:
∠QOP = ∠ORP = 90° (Angle in a semi-circle)
∴ OQ ⊥ QP and OR ⊥ RP. (We know that the line joining the centre of a circle to the tangent is always perpendicular)
Hence, we have PQ and PR as the tangents to the given circle.
☛ Check: NCERT Solutions Class 10 Maths Chapter 11
Video Solution:
Draw a circle with the help of a bangle. Take a point outside the circle. Construct the pair of tangents from this point to the circle.
NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.2 Question 7
Summary:
A circle was drawn with the help of a bangle. PQ and PR are the required tangents constructed to the given circle from a point P outside the circle.
☛ Related Questions:
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