Question 1 : In the given figure, if ∠DAB = 60° and ∠ABD = 50° then ∠ACB is equal to<br/>
<img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5ef19e6b819305523f232922"/>
Question 2 : In the given figure, O is the centre of the circle. If ∠ABC = 20°, then ∠AOC is equal to<br/>
<img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5ef19e69819305523f23291f"/>
Question 3 :
If the areas of two similar triangles are in the ratio 4 : 9, then their corresponding sides are in the ratio<br/>
Question 4 :
If in two triangles ABC and PQR,<br/> {tex}\frac { AB }{ QR } =\frac { BC }{ PR } =\frac { CA }{ PQ } {/tex}<br/> then<br/>
Question 5 : In the given figure, ∆ABC ~ ∆QPR. Then ∠R is<br/>
<img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5ef19e5a1766ce1c2c83a5c7"/>
Question 6 :
D and E are respectively the points on the sides AB and AC of a ∆ABC such that AD = 2 cm, BD = 3 cm, BC = 7.5 cm and DE || BC. Then the length of DE is<br/>
Question 7 :
From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is<br/>
Question 8 : The given figure, AB || DE. The length of CD is<br/>
<img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5ef19e5e1766ce1c2c83a5cf"/>
Question 9 : In the given figure, PQ || CA and all lengths are given in centimetres. The length of BC is<br/>
<img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5ef19e601766ce1c2c83a5d4"/>
Question 10 :
If ∆ABC ~ ∆PQR, area of ∆ABC = 81 cm², area of ∆PQR = 144 cm² and QR = 6 cm, then length of BC is<br/>
Question 11 : In the given figure, two line segments AC and BD intersect each other at the point P such that PA = 6 cm, PB = 3 cm, PC = 2.5 cm, PD = 5 cm, ∠APB = 50° and ∠CDP = 30°. Then, ∠PBA is equal to<br/>
<img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5ef19e5c1766ce1c2c83a5ca"/>
Question 12 :
It is given that ∆ABC ~ ∆PQR with {tex}\frac { BC }{ QR } =\frac { 1 }{ 3 } {/tex} then {tex}\frac { area\quad of\quad \Delta PQR }{ area\quad of\quad \Delta ABC } {/tex} equal to<br/>
Question 13 : In the given figure, two circles touch each other at A. BC and AP are common tangents to these circles. If BP = 3.8 cm, then the length of BC is equal to<br/>
<img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5ef19e7c819305523f232941"/>
Question 14 :
If ∆ABC ~ ∆QRP, {tex}\frac { area\quad of\quad \Delta ABC }{ area\quad of\quad \Delta PQR } = \frac {9}{4} {/tex}, AB = 18 cm and BC = 15 cm, then the length of PR is equal to<br/>
Question 15 :
If tangents PA and PB from an exterior point P to a circle with centre O are inclined to each other at an angle of 80°, then ∠POA is equal to<br/>
Question 16 :
If the angle between two radii of a circle is 130°, the angle between the tangents at the ends of the radii is<br/>
Question 17 : In the given figure, ∆ABC ~ ∆QPR. The value of x is<br/>
<img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5ef19e5bd586141c136a5d42"/>
Question 18 :
The areas of two similar triangles are 81 cm² and 49 cm² respectively. If an altitude of the smaller triangle is 3.5 cm, then the corresponding altitude of the bigger triangle is<br/>
Question 19 :
If ∆ABC ~ ∆PQR, BC = 8 cm and QR = 6 cm, then the ratio of the areas of ∆ABC and ∆PQR is<br/>
Question 20 : In the given figure, sides BC, CA and AB of ∆ABC touch a circle at the points P, Q and R respectively. If PC = 5 cm, AR = 4 cm and RB = 6 cm, then the perimeter of ∆ABC is<br/>
<img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5ef19e786150ce6eb5a14705"/>
Question 21 : In the given figure, O is the centre of a circle. If the length of chord PQ is equal to the radius of the circle, then ∠PRQ is<br/>
<img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5ef19e6e819305523f232929"/>
Question 22 : In the given figure, DE || BC and all measurements are in centimetres. The length of AE is<br/>
<img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5ef19e60d586141c136a5d4c"/>
Question 23 : In the given figure, if D, E and F are midpoints of the sides BC, CA and AB respectively, then the two triangles ABC and DEF are<br/>
<img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5ef19e5dd586141c136a5d47"/>
Question 24 : In the given figure, O is the centre of a circle and PQ is a chord. If the tangent PR at P makes an angle of 50° with PQ, then ∠POQ is<br/>
<img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5ef19e75819305523f232937"/>
Question 25 : In the given figure, PQ and PR are tangents from P to a circle with centre O. If ∠POR = 55°, then ∠QPR is<br/>
<img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5ef19e716150ce6eb5a146f9"/>
Question 26 : In the given figure, {tex} \mathrm{O} {/tex} is the centre of the circle and {tex} \mathrm{DF} {/tex} is the tangent at {tex} \mathrm{E} {/tex}. If {tex} \angle \mathrm{CBE}=25^{\circ}, {/tex} find {tex} \angle \mathrm{CDE}+\angle \mathrm{CED} {/tex}<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5fb79e3bdba5935f6cc6ee26"><br>
Question 27 :
Two circles are of radii {tex} 3 \mathrm{~cm} {/tex} and {tex} 3 \mathrm{~cm} {/tex}. If the distance between their centres is {tex} 10 \mathrm{~cm} {/tex}, what is the length of their transverse common tangent?
Question 28 :
The angle between a tangent to a circle and the radius drawn at the point of contact is
Question 29 : Two chords AB and CD of a circle intersect externally at a point P. If PC = 15 cm, CD = 7 cm and AP = 12 cm, then AB is<br/>
<img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5ef19e7e819305523f232946"/>
Question 30 : In the given figure, DE || CA and D is a point on BD such that BD : DC = 2 : 1. The ratio of area of ∆ABC to area of ∆BDE is<br/>
<img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5ef19e67d586141c136a5d57"/>
