Intersection between Secants

Q.

A line intersecting a circle in two points is called_________

Q.

In the figure, $PA$ is a tangent to the circle. $PBC$ is secant and $AD$ bisects angle $BAC$. Select the statements that are true.

1. $\angle CAD=\frac{1}{3}(\angle PBA-\angle PAB)$

2. Triangle PAD is an isoscles triangle

3. $\angle CAD=\frac{1}{2}(\angle PBA-\angle PAB)$

4. $\angle CAD=\frac{1}{9}(\angle PBA-\angle PAB)$

Q. Form the pair of linear equations in the following problems, and find their solutions graphically.
(i) $10$ students of Class X took part in a Mathematics quiz. If the number of girls is $4$ more than the number of boys, find the number of boys and girls who took part in the quiz.
(ii) $5$ pencils and $7$ pens together cost Rs $50,$ whereas $7$ pencils and $5$ pens together cost Rs $46.$ Find the cost of one pencil and that of one pen.

Q. In the given figure, chords AB and CD when extended meet at P. If AB = 4 cm, BP = 6 cm, DP = 5 cm, then CD =______.

1. 12 cm
2. 10 cm
3. 8 cm
4. 7 cm

Q.

In the given figure chords AB and CD intersect at P. If PA = x, PB =9cm, PC =5 cm and PD = 8.1cm, find the value of ‘x’.

1. 5.5 cm

2. 4.5 cm

3. 4 cm

4. 1 cm

Q.

In the given figure, AE and BC intersect each other at point D. If $\angle CDE={90}^0$, AB = 5cm, BD = 4cm and CD = 9 cm, find AE.

1. 20 cm

2. 10 cm

3. 13 cm

4. 15 cm

Q. Expalain Thales theorem

Q.

The perimeter of a right triangle is equal to the sum of the diameter of its incircle and twice the diameter of its circumcircle.

1. True

2. False

Q. In the given figure, if PQ = 6, QR = 10, PS = 8 find TS.

Q.

Find the unknown length 'Y' in the given figure.

1. 24 cm

2. 16 cm

3. 8 cm

4. 32 cm

Q.

In the given figure AB and DC are two chords of a circle with centre O, which when produced meet at P. If PB = 7 cm, BA = 10 cm and PO =12cm, find the radius of the circle.

1. 12 cm

2. 10 cm

3. 5 cm

4. 6 cm

Q. Prove that the tangent drawn at the mid-point of an arc of a circle is parallel to the chord joining the end points of the arc.

Q.

Find the unknown length x of the following figure.

1. 2 cm

2. 10 cm

3. 12 cm

4. 18 cm

Q.

Two chords AP and QM of a circle intersect internally at a point R. If AR = 14 cm, RP = 9 cm, and RQ = 21 cm, then find MR.

1. 9 cm

2. 2 cm

3. 4 cm

4. 6 cm

Q. In the given figure, chord MN and chord RS intersect at point D.
(1) If RD = 15, DS = 4,
MD = 8 find DN
(2) If RS = 18, MD = 9,
DN = 8 find DS

Q.

In the given figure, AC = AE.

Show that :

(i) CP = EP

(ii) BP = DP.

Q. In the given figure, m(arc WY) = 44°, m(arc ZX) = 68°, then
(1) Find the measure of ∠ ZTX.
(2) If WT = 4.8, TX = 8.0,
YT = 6.4, find TZ.
(3) If WX = 25, YT = 8,
YZ = 26, find WT.

Q.

In the figure $△ABC$ is a right angled triangle with right angle at B. BD is perpendicular to AC. Then which of the following options will hold true?

1. $A{B}^2=AD\times DC$

2. $A{B}^2=AD\times AC$

3. $A{D}^2=DC\times AC$

4. $A{B}^2=D{C}^2+A{D}^2$

Q.

A chord of a circle of radius 12 cm subtends an angle of ${120}^{\circ }$ at the centre. Find the area in $c{m}^2$ of the corresponding segment of the circle. (Use $\pi =3.14$ and $\sqrt{3}=1.73$) [3 MARKS]

Q.

ABCD is a cyclic quadrilateral in which BC is parallel to AD, angle ADC = ${110}^0$ and angle BAC = ${50}^0$. Select the statements that are true.

1. $\angle DAC={60}^o$

2. $\angle DCA={20}^o$

3. $\angle DCA={10}^o$

4. $\angle DAC={50}^o$

Q. In the given figure
(1) m(arc CE) = 54°, m(arc BD) = 23°, find measure of ∠CAE.
(2) If AB = 4.2, BC = 5.4, AE = 12.0, find AD
(3) If AB = 3.6, AC = 9.0, AD = 5.4, find AE

Q.

Find the relation between the perimeter of a right triangle with the diameter of its incircle and circumcircle.

Q.

Prove that the perimeter of a right triangle is equal to the sum of the diameter of its incircle and twice the diameter of its circumcircle.

Q.

Find the unknown length 'Z' of the following figure when BC = 4 cm, CD = 3 cm, and ED = 13 cm.

1. 8 cm

2. 9 cm

3. 10 cm

4. 4 cm

Q.

In the given figure, chords AB and CD when extended meet at P. If AB = 4 cm, BP = 6 cm, DP = 5 cm, then CD =__.

1. 12 cm
2. 10 cm
3. 8 cm
4. 7 cm

Q.

In the given figure, AE and BC intersect each other at point D.

If $\angle$ CDE = ${90}^o$ , AB = 5 cm, BD = 4 cm and CD = 9 cm, find AE.

1. <!--td {border: 1px solid #cccccc;}br {mso-data-placement:same-cell;}--> $$8cm$$
2. $$12cm$$
3. $$9cm$$
4. $$15cm$$

Q.

ABC is a right triangle, right angled at B. A circle is inscribed in it. The lengths of the two sides containing the right angle are 6 cm and 8 cm. Find the radius of the incircle. [4 MARKS]

Q. In the given figure, chords AB and CD when extended meet at P. If AB = 4 cm, BP = 6 cm, DP = 5 cm, then find the value of CD.

Q.

Two chords AP and QM of a circle intersect internally at a point R. If AR = 21 cm, RP = 9 cm, and PQ = 21 cm, then find MR.

1. 2 cm

2. 4 cm

3. 6 cm

4. 9 cm

Q.

In the given figure, $\angle CAB={90}^o$ and $AD\perp BC$. Show that $\Delta BDA\sim \Delta BAC$. If AC = 75 cm, AB = 1 m and BC = 1.25 m, find AD.