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Andhra Pradesh SSC (Class 10) Triangles and Circles — practice questions

Explore 50 free Triangles and Circles questions in Andhra Pradesh SSC (Class 10) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Triangles and Circles questions and exercises with answers

Showing questions 1–30 of 50.

If two angles of one triangle are respectively equal to two angles of another triangle, then the triangles are similar by theRead the answer and worked solution →If tangents $PA$ and $PB$ from a point $P$ to a circle with centre $O$ are inclined to each other at an angle of $80^\circ$, then $\angle POA$ isRead the answer and worked solution →From a point $Q$, the length of the tangent to a circle is $24\text{ cm}$ and the distance of $Q$ from the centre is $25\text{ cm}$. The radius of the circle isRead the answer and worked solution →The common point of a tangent and a circle is called theRead the answer and worked solution →If XY is a tangent to a circle with centre O at point P, then $OP$ isRead the answer and worked solution →At a given point on a circle, how many tangents can be drawn?Read the answer and worked solution →A line that intersects a circle at exactly two distinct points is called aRead the answer and worked solution →Two triangles are similar if:Read the answer and worked solution →By the Pythagoras theorem, in a right-angled triangle:Read the answer and worked solution →A tangent to a circle is:Read the answer and worked solution →From a point outside a circle, the two tangents drawn are:Read the answer and worked solution →CLASS10 · Mathematics · Similarity Criteria — TrianglesRead the answer and worked solution →CLASS10 · Mathematics · Circles — True or FalseRead the answer and worked solution →Two figures are said to be similar if they haveRead the answer and worked solution →All circles areRead the answer and worked solution →All squares with different side lengths areRead the answer and worked solution →The criterion that uses two pairs of equal angles to prove triangle similarity is calledRead the answer and worked solution →In two similar triangles, the ratio of corresponding sides is calledRead the answer and worked solution →Pythagoras theorem applies to which triangles?Read the answer and worked solution →In triangle ABC, DE is parallel to BC where D lies on AB and E on AC. If AD = 2 cm, DB = 3 cm and AE = 4 cm, then EC equalsRead the answer and worked solution →Two triangles have areas in the ratio 49 : 64. The ratio of their corresponding sides isRead the answer and worked solution →A vertical pole 6 m tall casts a shadow 4 m long at the same time a tower casts a shadow 28 m long. The height of the tower isRead the answer and worked solution →In a right triangle the legs measure 9 cm and 12 cm. The hypotenuse isRead the answer and worked solution →If two triangles are similar and the ratio of their perimeters is 3 : 5, then the ratio of their areas isRead the answer and worked solution →In triangle ABC, AD bisects angle A and meets BC at D. If AB = 6 cm, AC = 9 cm and BC = 10 cm, then BD equalsRead the answer and worked solution →The hypotenuse of a right triangle is 26 cm and one leg is 24 cm. The other leg isRead the answer and worked solution →The altitude AD of an equilateral triangle ABC of side length a isRead the answer and worked solution →In triangle PQR, S and T are points on PQ and PR respectively. ST is parallel to QR. If PS = 3, SQ = 6 and PT = 4, then PR equalsRead the answer and worked solution →A 5 m long ladder leans against a wall with its foot 3 m from the wall. The height it reaches up the wall isRead the answer and worked solution →The diagonals of a rhombus are 16 cm and 30 cm. The length of each side isRead the answer and worked solution →

Worked practice questions

If two angles of one triangle are respectively equal to two angles of another triangle, then the triangles are similar by the

  1. SSS similarity criterion
  2. SAS similarity criterion
  3. AA similarity criterion
  4. RHS congruency criterion
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Correct answer: C. AA similarity criterion

If two corresponding angles are equal, then the third angles are also equal by the angle sum property of a triangle. **Hence the triangles are similar by the AA criterion.**

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If tangents $PA$ and $PB$ from a point $P$ to a circle with centre $O$ are inclined to each other at an angle of $80^\circ$, then $\angle POA$ is

  1. $50^\circ$
  2. $60^\circ$
  3. $70^\circ$
  4. $80^\circ$
Show answer and solution

Correct answer: A. $50^\circ$

Since tangents from an external point are equal, $PA = PB$, and also $OA = OB$. Hence triangles $OAP$ and $OBP$ are congruent, so $OP$ bisects $\angle APB$. Therefore $\angle APO = 40^\circ$. In right triangle $OAP$, $\angle OAP = 90^\circ$ because radius is perpendicular to tangent so $\angle POA = 180^\circ - 90^\circ - 40^\circ = 50^\circ$.

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From a point $Q$, the length of the tangent to a circle is $24\text{ cm}$ and the distance of $Q$ from the centre is $25\text{ cm}$. The radius of the circle is

  1. $7\text{ cm}$
  2. $12\text{ cm}$
  3. $15\text{ cm}$
  4. $24.5\text{ cm}$
Show answer and solution

Correct answer: A. $7\text{ cm}$

The radius to the point of contact is perpendicular to the tangent, so the triangle formed is right-angled. If radius is $r$, then $25^2 = 24^2 + r^2$. Thus $r^2 = 625 - 576 = 49$, so $r = 7\text{ cm}$. Options B, C and D do not satisfy the Pythagorean relation.

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More Mathematics topics

Real Numbers and PolynomialsArithmetic ProgressionStatistics and ProbabilityQuadratic EquationsLinear Equations in Two VariablesIntroduction to TrigonometrySurface Areas and VolumesAreas Related to Circles