alleryPA,PB touch a circle at A,B; centre O has minor ∠AOB=110°. Find ∠APB.
- 110°
- 55°
- 140°
- 70°
Show answer and solution
Correct answer: D. 70°
The two right angles at A and B give ∠APB=180°−110°=70°.
ICSE Class 10 Geometry: Similarity, Circles & Loci — practice questions — page 4
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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PA,PB touch a circle at A,B; centre O has minor ∠AOB=110°. Find ∠APB.Read the answer and worked solution →PA,PB are tangents from P to a circle centred at O. If ∠APB=64°, ∠APO isRead the answer and worked solution →ABC has sides AB=13,BC=14,CA=15 cm. Its incircle touches AB at T. AT?Read the answer and worked solution →A circle touches all four sides of convex ABCD; AB=6,BC=8,CD=10 cm. DA?Read the answer and worked solution →P,A,B lie in that order on a secant; PA=4,AB=5 cm. Tangent PT has lengthRead the answer and worked solution →Secants P,A,B and P,C,D have PA=3,PB=12,PC=4 cm in those orders. CD?Read the answer and worked solution →Two secants from P cut a circle: first outer x,inner 7; second outer 3,whole 10 cm. x?Read the answer and worked solution →Chords AB,CD meet inside at P; PA=3,PB=8,CD=10 cm, PC<PD. PC?Read the answer and worked solution →PT=12 cm is tangent to a radius-5 cm circle. A is its nearest point to P. PA?Read the answer and worked solution →Convex cyclic ABCD has AB∥CD and ∠DAB=70°. What is ∠ABC?Read the answer and worked solution →Which consecutive-angle list can describe a convex cyclic quadrilateral?Read the answer and worked solution →O is a circle's centre; A,B lie on it, ∠OAB=35°. C lies on major arc AB. ∠ACB?Read the answer and worked solution →A,B,C lie on a circle centred at O; ∠ACB=120°. Minor ∠AOB equalsRead the answer and worked solution →A,B,P,Q lie on a circle, P,Q on opposite sides of AB. ∠APB=68°. ∠AQB?Read the answer and worked solution →AB is a diameter, C another circle point; AC=5,BC=12 cm. Circle radius?Read the answer and worked solution →At A on a circle centred O, the tangent makes 50° with chord AB. ∠OAB?Read the answer and worked solution →C is on major arc AB; tangent at A makes 50° with AB, ∠ABC=60°. ∠BAC?Read the answer and worked solution →Distinct parallel tangents touch a radius-r circle at A,B. AB has lengthRead the answer and worked solution →BC is a diameter of the circle through A,B,C, and AB=AC. ∠ABC?Read the answer and worked solution →Tangents PA,PB touch a circle centred O. The circle through O,A,P,B has diameterRead the answer and worked solution →A,B,C are distinct points on a circle; ∠ACB=90°. What must AB be?Read the answer and worked solution →Where is the circumcentre when constructing the circumcircle of an acute triangle?Read the answer and worked solution →For an obtuse triangle, where must its circumcircle's centre be placed?Read the answer and worked solution →Where is a right triangle's circumcentre?Read the answer and worked solution →Set the compass point at a triangle's circumcentre. Which opening draws its circumcircle?Read the answer and worked solution →Which condition verifies a constructed circle is a triangle's incircle?Read the answer and worked solution →In a nondegenerate triangle, its incircle's centre must lieRead the answer and worked solution →Match each tangent calculation with its result:Read the answer and worked solution →Match each cyclic quadrilateral property with its rule:Read the answer and worked solution →Match each circle intersection feature with its name:Read the answer and worked solution →
Worked practice questions
PA,PB are tangents from P to a circle centred at O. If ∠APB=64°, ∠APO is
- 32°
- 58°
- 64°
- 128°
Show answer and solution
Correct answer: A. 32°
The line PO bisects the angle between the two tangent segments, giving 64°/2=32°.
ABC has sides AB=13,BC=14,CA=15 cm. Its incircle touches AB at T. AT?
- 7 cm
- 8 cm
- 6 cm
- 9 cm
Show answer and solution
Correct answer: A. 7 cm
Equal tangent segments from each vertex give AT=(13+15−14)/2=7 cm.
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