Length of Tangents Drawn from an External Point

Q. Question 6
PQ and RS are two mirrors placed parallel to each other. An incident ray AB strikes the mirror PQ at B, the reflected ray moves along the path BC and strikes the mirror RS at C and again reflects back along CD. Prove that AB||CD

Q.

If the angle between two tangents drawn from an external point P to a circle of radius a and centre O is 60 then find the length of OP

Q.

In fig., PA and PB are two tangents drawn from an external point P to a circle with centre C and radius 4 cm. If PA ⊥ PB, then the length of each tangent is:

1. 5 cm

2. 6 cm

3. 4 cm

4. 3 cm

Q.

ABC is a right angled triangle with AB = 12 cm and AC = 13 cm. A circle, with centre O, has been inscribed inside the triangle.

Calculate the value of x, the radius of the inscribed circle.

1. 8 cm

2. 3 cm

3. 2 cm

4. 9 cm

Q.

In the given figure, PA and PB are tangents drawn from an external point P to a circle. CD is the third tangent touching the circle at Q. If PB=10cm and CQ=2cm, then the length of PC is:

1. 12 cm

2. 14 cm

3. 8 cm

4. 10 cm

Q.

From the figure find the length of the tangent CD given AP = 3 cm, and PC = 8 cm.

Q.

Question 3
From an external point P, two tangents , PA and PB are drawn to a circle with centre O. At one point E on the circle tangent is drawn which intersects PA and PB at C and D, respectively. If PA = 10 cm, find the perimeter of the triangle PCD.

Q.

In the figure PQ and PR are tangents to the circle with centre ‘O’. If , shown that PQOR is a square.

Q.

In figure, XP and XQ are two tangents to a circle with center O from a point X outside the circle. ARB is tangent to circle at R. Prove that XA + AR = XB + BR.

Q.

what are the seven circle theorems?

Q.

In the figure PQ and PR are tangents to the circle with centre ‘O’. If , shown that PQOR is a square.

Q. Calculate the length of tangent from a point $15cm$ away from the circle of a circle of radius $9cm$.

Q.

From an external point P, two tangents are drawn that touches the circle at points Q and R. The triangle PQR is a/an___ triangle.

1. Equilateral

2. Isosceles

3. Scalene

4. Right angled

Q. Prove that the length of tangents drawn from an external point to a circle are equal.

Q.

From the figure find the length of the tangent CD given AP = 3 cm, and PC = 8 cm.

Q.

In the given figure, XY and X’Y’ are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and X’Y’ at B. Prove that ∠AOB=90.

Q.

In the figure AT and BT are the tangents to a circle with centre O. Another tangent PQ is drawn such that TP = TQ. Show that ΔTAB ||| ΔTPQ.

Q. The tangent at a point C of a circle and a diameter ab when extended intersect it p. If angle PCA = 110, find angle CBA

Q.

A circle touches all the sides of quadrilateral ABCD . If AB=8, BC=10 & CD=7, then find AD.

Q.

Find the radius of the circle with centre O. PT is a tangent and AB is perpendicular to PT. PA and PB is 4 cm and 2 cm respectively.

1. 4 cm

2. 2 cm

3. 6 cm

4. 3 cm

Q. In the given figure, a quadrilateral ABCD is drawn to circumscribe a circle such that its side AB, BC, CD and AD touch the circle at P, Q, R and S respectively. If AB = x cm, BC = 7 cm, CR = 3 cm and AS = 5 cm , find x

Q. Two tangents making an angle of 120 with each other are drawn to a circle of radius, find the length of each tangent.

Q.

In the given figure a triangle ABC is drawn to circumscribe a circle of radius 3 cm such that the segments BD and DC into which BC is divided by the point of contact D are of length 9 cm and 3 cm respectively. Find the length of sides AB and AC.

1. AB = 9 cm, AC = 15 cm
2. AB = 10 cm, AC = 5 cm
3. AB = 5 cm, AC = 10 cm
4. AB = 15 cm, AC = 9 cm

Q.

In the figure AT and BT are the tangents to a circle with centre O. Another tangent PQ is drawn such that TP = TQ. Show that ΔTAB ||| ΔTPQ.

Q. If two tangents AP and AQ are drawn to a circle with centre 'O' from an external point A, then

1. ∠PAQ = ∠OPQ = ∠OQP
2. ∠PAQ = 2∠OPQ = 2∠OQP
3. 2∠PAQ =∠OPQ = ∠OQP
4. ∠PAQ = 0.5∠OPQ = 0.5∠OQP

Q. Prove that the tangents drawn at the ends of a diameter ofa circle are parallel.

Q. $\text{In the given figure, a circle touches the}\text{side BC of}\Delta ABC\text{at P. AR and AQ are}\text{two tangents drawn from a point A}\text{outside the circle. If AQ = 15 cm, find}\text{the perimeter of}\Delta ABC\text{(in cm)}.$

1. 30

Q.

The sides of a quadrilateral ABCD are tangents to the circle with centre ‘O’. If AB = 8 cm and CD = 5 cm find AD + BC.

Q. Tangent drawn at the midpoint of an arc of a circle is parallel to the chord joining the end points of the arc.

1. True
2. False

Q. Prove that the parallelogram circumscribing a circle is a rhombus.
Or, ∆ABC is drawn to circumscribe a circle of radius 4 cm, such that the segments BD and DC into which BC is divided by the point of contact D, are of lengths 8 cm and 6 cm respectively. Find AB and AC.
Figure