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ICSE Class 10 Geometry: Similarity, Circles & Loci — practice questions — page 3

Explore 121 free Geometry: Similarity, Circles & Loci questions in ICSE Class 10 Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Geometry: Similarity, Circles & Loci questions and exercises with answers

Showing questions 61–90 of 121.

Two restrictions both require P to lie4cm from O in a plane. How many positions remain?Read the answer and worked solution →AB=6cm. A plane point P is equidistant from A and B and3cm from A. Where is P?Read the answer and worked solution →PA=PB=13cm and AB=10cm. If M is the midpoint of AB, what is PM?Read the answer and worked solution →Inside a60° angle at O, P is equidistant from its sides and2cm from O. How many positions?Read the answer and worked solution →In ABC, A=40°,B=60°; in PQR, P=80°,Q=40°. Which ordered similarity is valid?Read the answer and worked solution →Which change always produces a shape similar to the original?Read the answer and worked solution →Two rectangles are 2×3 cm and 4×5 cm. What prevents similarity?Read the answer and worked solution →Which relation must hold for two congruent triangles?Read the answer and worked solution →Do equal perimeters establish triangle similarity?Read the answer and worked solution →A~B with side ratio 2:3; B~C with side ratio 4:5. Find A:C side ratio.Read the answer and worked solution →Corresponding lengths of a shape rise by 20% uniformly. Its area rises byRead the answer and worked solution →Similar triangles' sides are 2:3; their areas differ by 25 cm². Smaller area?Read the answer and worked solution →Similar triangles have corresponding altitudes 9,15 cm. Smaller area is 27 cm². Larger?Read the answer and worked solution →At scale 1:10000, a park occupies 3 cm² on a map. Actual area?Read the answer and worked solution →The same road appears on maps scaled 1:1000 and 1:2500. First:second map lengths?Read the answer and worked solution →A similar model facade is 1:20 in length. Actual paintable area is 12 m². Model area?Read the answer and worked solution →Similar triangles' corresponding sides are 4:7. Corresponding medians are in ratioRead the answer and worked solution →In ABC, D∈AB, E∈AC; AD=3,DB=2,AE=6,EC=4. Which follows?Read the answer and worked solution →D∈AB, E∈AC in ABC, DE∥BC; AD:DB=2:3 and BC=15 cm. DE?Read the answer and worked solution →In ABC, D∈AB,E∈AC, DE∥BC, AD:AB=2:3. Area ADE:area DBCE?Read the answer and worked solution →D,E are midpoints of AB,AC in ABC. If BC=18 cm, DE equalsRead the answer and worked solution →In ABC, D∈AB,E∈AC, DE∥BC. AD=x,DB=3,AE=x+1,EC=4. Find x.Read the answer and worked solution →In ABC, DE∥FG∥BC; D,F∈AB, E,G∈AC. AD:AF=2:3. Find DE:FG.Read the answer and worked solution →In convex trapezium ABCD, AB∥CD. Diagonals meet at O; AB:CD=2:3. AO:OC?Read the answer and worked solution →Two triangles have the same altitude; their bases are 2:3. Their areas areRead the answer and worked solution →ABC~DEF in that order, AB:DE=2:3 and AC=10 cm. Which side is 15 cm?Read the answer and worked solution →Tangent counts through a point inside, on, outside a circle, respectively?Read the answer and worked solution →Circles of radii 7,3 cm touch externally. Their centres are separated byRead the answer and worked solution →A radius-3 cm circle touches a radius-8 cm circle internally. Centre distance?Read the answer and worked solution →PT is tangent at T; centre O has OT=5 cm, OP=13 cm. PT equalsRead the answer and worked solution →

Worked practice questions

Two restrictions both require P to lie4cm from O in a plane. How many positions remain?

  1. No such point
  2. Exactly two
  3. Infinitely many
  4. Exactly one
Show answer and solution

Correct answer: C. Infinitely many

The restrictions define the same circle, so every point on that circle satisfies both.

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AB=6cm. A plane point P is equidistant from A and B and3cm from A. Where is P?

  1. At endpoint B of AB
  2. Outside the segment AB
  3. At the midpoint of AB
  4. At endpoint A of AB
Show answer and solution

Correct answer: C. At the midpoint of AB

The circle about A touches the perpendicular bisector of AB at its midpoint,3cm from A.

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PA=PB=13cm and AB=10cm. If M is the midpoint of AB, what is PM?

  1. 12cm
  2. 8cm
  3. 13cm
  4. 18cm
Show answer and solution

Correct answer: A. 12cm

PM is perpendicular to AB, so PM²=13²−5²=144cm².

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