# Secant

## Trending Questions

**Q.**

Two tangents PA and PB are drawn to a circle with center O from an external point P. Prove that ∠APB=2∠OAB [3 MARKS]

**Q.**

A line which cuts a circle at two distinct points is called the

**Q.**In a circle, two chords AB and CD intersect at a point inside the circle. Prove that

$\left(\mathrm{a}\right)\u25b3\mathrm{PAC}~\u25b3\mathrm{PDB}\phantom{\rule{0ex}{0ex}}\left(\mathrm{b}\right)\mathrm{PA}.\mathrm{PB}=\mathrm{PC}.\mathrm{PD}$

**Q.**

In the given figure, PT is a common tangent to the circles touching externally at P and AB is another common tangent touching the circles at A and B. Prove that: [3 MARKS]

(i) T is the mid-point of AB

(ii) ∠APB=90∘

(iii) If X and Y are centers of the two circles, show that the circle on AB as diameter touches the line XY.

**Q.**Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact

**Q.**

The angle between the curves $y={a}^{x}$ and $y={b}^{x}$ is equal to

${\mathrm{tan}}^{-1}\left|\frac{\left(a-b\right)}{1+ab}\right|$

${\mathrm{tan}}^{-1}\left|\frac{\left(a-b\right)}{1-ab}\right|$

${\mathrm{tan}}^{-1}\left|\frac{\left(\mathrm{log}b+\mathrm{log}a\right)}{1+\mathrm{log}a\mathrm{log}b}\right|$

${\mathrm{tan}}^{-1}\left|\frac{\left(\mathrm{log}b+\mathrm{log}a\right)}{1-\mathrm{log}a\mathrm{log}b}\right|$

${\mathrm{tan}}^{-1}\left|\frac{\left(\mathrm{log}b-\mathrm{log}a\right)}{1+\mathrm{log}a\mathrm{log}b}\right|$

**Q.**If two circles are touching externally, how many common tangents of them can be drawn?

- One
- Two
- Three
- Four

**Q.**

Two chords AB and AC of a circle are equal. Prove that the centre of the circle lies on the bisector of angle BAC.

Show that the bisector of angle BAC is a perpendicular bisector of chord BC

**Q.**In the given figure, O is the centre of a circle, chord PQ ≅ chord RS If ∠ POR = 70° and (arc RS) = 80°, find –

(1)

*m*(arc PR)

(2)

*m*(arc QS)

(3)

*m*(arc QSR)

**Q.**Question 7

In figure, tangents PQ and PR are drawn to a circle such that ∠RPQ=30∘. A chord RS is drawn parallel to the tangent PQ. Find the ∠ RQS.

**Q.**

In the figure, PT touches a circle with center O at R. Diameter SQ when produced meets RT at P. ∠SPR = ^{o}, ∠QRP = y^{o}, find the value of ^{o} + 2y^{o}.

180

^{o}360

^{o}270

^{o}90

^{o}30

^{o}

**Q.**Question 10

AB is a diameter of a circle and AC is the chord such that ∠ BAC = 30∘. If the tangent at C intersects AB extended at D, then BC = BD.

**Q.**______ is a line that touches a circle at only one point, and ______ is a line that intersects a circle at two distinct points.

- Tangent, secant
- Secant, secant
- Secant, tangent
- Tangent, tangent

**Q.**______ is a line that touches a circle at only one point, and ______ is a line that intersects a circle at two distinct points.

- Secant, secant
- Secant, tangent
- Tangent, tangent
- Tangent, secant

**Q.**

In the given figure, two chords AB and CD intersect each other at the point P. prove that:

(i) ΔAPC ∼ ΔDPB

(ii) AP.BP = CP.DP

**Q.**

Which of the following statements is/are correct?

1. With respect to a tangent both the circles lie on the same side, this tangent is called direct common tangent.

2. With respect to a tangent both the circles lie on the opposite side, this tangent is called transverse (indirect) common tangent.

Only 2

Only 1

Both 1 & 2

None of these

**Q.**

**Question 5**

At one end A of a diameter AB of a circle of radius 5 cm, tangent XAY is drawn to the circle. The length of the chord CD parallel to XY and at a distance 8 cm from A, is

(A) 4 cm

(B) 5 cm

(C) 6 cm

(D) 8 cm

**Q.**

A line which cuts a circle at two distinct points is called the

**Q.**

A line that intersects a circle in two distinct points is called a

Tangent

Diameter

Chord

Secant

**Q.**In figure. If PQR is the tangent to a circle at Q whose centre is O, AB is a chord parallel to PR and ∠BQR=70∘ , then ∠AQB is equal to

**Q.**

The angle of elevation of the top of a tower from a point P on the ground is α. After walking a distance d towards the foot of the tower, angle of elevation is found to be β. Then:

None of these

α > β

α = β

α < β

**Q.**Explain the theorem of tangent line

**Q.**

- Tangent
- Secant
- Chord

**Q.**

- Tangent
- Secant
- Chord

**Q.**

When a chord divides a circle into two parts, each part is called a:

Chord

Segment

Secant

Centre

**Q.**A line that touches a circle at exactly one point is called a ______.

- tangent
- secant
- diameter
- radius

**Q.**

___ is a line that intersects a circle at only one point, and ___ is a line that intersects a circle at two distinct points.

Tangent, secant

Secant, secant

Secant, tangent

Tangent tangent

**Q.**

A___ is a line and a ___ is a line segment.

secant, chord

chord , secant

diameter, radius

radius, diameter

**Q.**______ is a line that touches a circle at only one point, and ______ is a line that intersects a circle at two distinct points.

- Tangent, secant
- Secant, secant
- Secant, tangent
- Tangent, tangent

**Q.**Prove that “ The perpendicular from the centre of a circle to a chord bisects the chord”