Tangents from a point to a circle
Draw a circle with center O and radius 2.5 cm, and a point P 6 cm from O. Construct the tangents from P to the circle.
Draw a circle with center O and radius 3 cm, and a point P 7 cm from O. Construct the tangents from P to the circle.
Draw a circle with center O and radius 2 cm, and a point P 5 cm from O. Construct the tangents from P to the circle.
Draw a circle with center O and radius 3 cm, and a point P 5.5 cm from O. Construct the tangents from P to the circle.
1. With O as the center and radius 2.5 cm, draw a circle. Mark P, 6 cm from O, and join OP.
2. Draw the perpendicular bisector of OP. It cuts OP at its midpoint M.
3. With M as the center and radius MO, draw a circle. It cuts the first circle at T and S.
4. Join PT and PS: they are the tangents from P.
1. With O as the center and radius 3 cm, draw a circle. Mark P, 7 cm from O, and join OP.
2. Draw the perpendicular bisector of OP. It cuts OP at its midpoint M.
3. With M as the center and radius MO, draw a circle. It cuts the first circle at T and S.
4. Join PT and PS: they are the tangents from P.
1. With O as the center and radius 2 cm, draw a circle. Mark P, 5 cm from O, and join OP.
2. Draw the perpendicular bisector of OP. It cuts OP at its midpoint M.
3. With M as the center and radius MO, draw a circle. It cuts the first circle at T and S.
4. Join PT and PS: they are the tangents from P.
1. With O as the center and radius 3 cm, draw a circle. Mark P, 5.5 cm from O, and join OP.
2. Draw the perpendicular bisector of OP. It cuts OP at its midpoint M.
3. With M as the center and radius MO, draw a circle. It cuts the first circle at T and S.
4. Join PT and PS: they are the tangents from P.
Why it works
T is on the circle with diameter OP, so ∠OTP = 90° (the angle in a semicircle). A line that meets a radius at 90° where it touches the circle is a tangent, so PT is one; PS is the other, the same length.