alleryOpposite angles of a cyclic quadrilateral are x° and 3x°. Find x.
- 60°
- 90°
- 45°
- 30°
Show answer and solution
Correct answer: C. 45°
The opposite angles sum to 180°, so 4x = 180° and x = 45°.
ICSE Class 10 Geometry: Similarity, Circles & Loci — practice questions — page 2
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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Opposite angles of a cyclic quadrilateral are x° and 3x°. Find x.Read the answer and worked solution →A radius meets a tangent at the point of contact. What angle do they form?Read the answer and worked solution →A tangent meets radius OP at P. If angle between them is x°, find x.Read the answer and worked solution →Two circles touch at P. Where do their centres and P lie?Read the answer and worked solution →From external point X, two tangents touch a circle at A and B. If XA is 9 cm, find XB.Read the answer and worked solution →Tangents from X have lengths 2x + 1 and 13 cm. Find x.Read the answer and worked solution →A tangent and chord meet at P. Their angle is 42°. What angle lies in the alternate segment?Read the answer and worked solution →A tangent-chord angle is 61°. Find the angle in its corresponding alternate segment.Read the answer and worked solution →Two chords cross; segments are 3, 8, 4, x cm. Find x.Read the answer and worked solution →Intersecting chords have segment lengths 2 cm, 12 cm and 3 cm, x cm. Find x.Read the answer and worked solution →Chords cross; one has segments 5, 6 cm, the other 4, x cm. Find x.Read the answer and worked solution →A cyclic quadrilateral has angles 2x° and 4x° opposite each other. Find x.Read the answer and worked solution →A tangent touches a circle at T. Which angle equals angle between tangent and chord TA?Read the answer and worked solution →One angle of a cyclic quadrilateral is 95°. What is the exterior angle at its opposite vertex?Read the answer and worked solution →What tools are allowed to construct a regular hexagon?Read the answer and worked solution →A regular hexagon is inscribed in a circle. What is each side length?Read the answer and worked solution →To locate a triangle’s circumcentre, which lines are constructed?Read the answer and worked solution →Which lines meet at the in-centre of a triangle?Read the answer and worked solution →How does an incircle radius meet a triangle side?Read the answer and worked solution →For tangents from P to a circle at O, what is drawn first?Read the answer and worked solution →For the tangent construction, M is the midpoint of OP. Which circle is drawn next?Read the answer and worked solution →A circle with diameter OP meets the given circle at T. Why is PT tangent there?Read the answer and worked solution →Two tangents are drawn from one external point. How do lengths compare?Read the answer and worked solution →What condition on opposite sides defines a parallelogram?Read the answer and worked solution →In a rhombus, how do the diagonals meet?Read the answer and worked solution →A rectangle is being constructed from its diagonals. Which fact is useful?Read the answer and worked solution →For an inscribed circle, how does its radius meet a side?Read the answer and worked solution →Two fixed points are7cm apart. How many locations lie3cm from one and4cm from the other?Read the answer and worked solution →For restrictions PA=8cm, PB=3cm and AB=5cm, how many positions can P occupy?Read the answer and worked solution →How many plane points are simultaneously3cm and5cm from the same point O?Read the answer and worked solution →
Worked practice questions
A radius meets a tangent at the point of contact. What angle do they form?
- 180°
- 90°
- 45°
- 60°
Show answer and solution
Correct answer: B. 90°
The radius through the contact point is perpendicular to the tangent.
A tangent meets radius OP at P. If angle between them is x°, find x.
- 45°
- 180°
- 0°
- 90°
Show answer and solution
Correct answer: D. 90°
The radius and tangent at the point of contact are perpendicular.
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