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# Draw Tangents To A Circle From An External Point, math Assignment Help

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Construction - Draw Tangents To A Circle From An External Point, math

**Case I:** When the centre of the circle is known.

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**Construction 3:** Draw two tangents to a circle (whose diameter is 6 cm) from a point P at a distance 9 cm from its centre. Also measure the length of two tangents.

**Steps of Construction: **

1. Draw a circle with centre O and whose radius is 3 cm.

2. Take a point P at a distance 9 cm from the centre O.

3. Join O with P i.e., OP = 9 cm.

4. Bisect OP at C or draw the right bisector of OP.

5. With C as centre and radius PC or OC describe another circle cutting the given circle at T and T.

6. Join PT and PT.

7. PT and PT are required tangents drawn from a point P to the given circle.

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**Case II:** When the centre of the circle is not known.

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**Construction 4: **Draw a circle of radius 2 cm and construct tangents to it from an external point P without using the centre.

**Steps of Construction: **

1. Draw a circle with radius 2 cm.

2. Through the external point P draw a secant PBA meeting the circle at A and B.

3. Bisect AP at O or draw the right bisector of AP.

4. Draw a semi-circle described on AP as diameter.

5. Through B draw BC ^ AP meeting the semi-circle at C.

6. With centre P and radius PC draw an arc cutting the given circle at T and T.

7. Join PT and PT' which are the required tangents.

**Construction 5:** Construct a circle of radius 3 cm and take a point P at a distance of 7.5 cm from its centre. From it, construct tangents to the circle without using its centre.

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**Steps of Construction: **

1. Draw a circle with centre O with radius 3 cm and P is a point at a distance 7.5 cm from O.

2. Draw a secant through P intersect the circle at A and B.

3. Produce AP to a point C such that PA = PC.

4. With BC as diameter, draw a semi circle.

5. At P, construct a perpendicular to BC to intersect the semi-circle at D.

6. With P as centre and PD as radius, draw an arc to intersect the given circle at T and T.

7. Join PT and PT. Then, PT and PT are the two required tangents from the point P to the given circle.

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**Case I:**When the centre of the circle is known.

**Construction 3:**Draw two tangents to a circle (whose diameter is 6 cm) from a point P at a distance 9 cm from its centre. Also measure the length of two tangents.

**Steps of Construction:**

**Case II:**When the centre of the circle is not known.

**Construction 4:**Draw a circle of radius 2 cm and construct tangents to it from an external point P without using the centre.

**Steps of Construction:**

**Construction 5:**Construct a circle of radius 3 cm and take a point P at a distance of 7.5 cm from its centre. From it, construct tangents to the circle without using its centre.

**Steps of Construction:**

**Live Math Experts: Help with**External Circle

**Assignments - Homework**

**Math Online Tutoring**: External Circle