PYQ Vault
EbooksTutor

Area of the triangle formed by two tangents to a circle and their chord of contact

This type of question, asked 5 times: 2021 Paper 8, 2021 Paper 23, 29 Jun 2022, 28 Jul 2022, 6 Apr 2023. All 5 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2021 Paper 8

    74
    Two tangents are drawn from a point PP to the circle x2+y2−2x−4y+4=0x^{2}+y^{2}- 2x- 4y+ 4 = 0, such that the angle between these tangents is tan⁡−1(125)\tan^{- 1}\left( \frac{12}{5} \right), where tan⁡−1(125)∈(0,π)\tan^{- 1}\left( \frac{12}{5} \right)\in (0,\pi). If the centre of the circle is denoted by CC and these tangents touch the circle at points AA and BB, then the ratio of the areas of △PAB\bigtriangleup PAB and △CAB\bigtriangleup CAB is:

    Tap an option to check your answer.

  2. Question 2

    2021 Paper 23

    89
    Let BB be the centre of the circle x2+y2−2x+4y+1=0x^{2}+y^{2}- 2x+ 4y+ 1 = 0. Let the tangents at two points PP and QQ on the circle intersect at the point A(3,1)A(3,1). Then 8. (area△APQarea△BPQ)\left( \frac{area \bigtriangleup APQ}{area \bigtriangleup BPQ} \right) is equal to

  3. Question 3

    29 Jun 2022

    79
    Let the tangent to the circle C1:x2+y2=2C_{1}:x^{2}+y^{2}= 2 at the point M(−1,1)M( - 1,1) intersect the circle C2C_{2} : (x−3)2+(y−2)2=5(x - 3)^{2}+ (y - 2)^{2}= 5, at two distinct points AA and BB. If the tangents to C2C_{2} at the points AA and BB intersect at NN, then the area of the triangle ANB is equal to:

    Tap an option to check your answer.

  4. Question 4

    28 Jul 2022

    163
    Let the tangents at two points AA and BB on the circle x2+y2−4x+3=0x^{2}+y^{2}- 4x + 3 = 0 meet at origin O(0,0)O(0,0). Then the area of the triangle of OABOAB is

    Tap an option to check your answer.

  5. Question 5

    6 Apr 2023

    167
    If the tangents at the points PP and QQ on the circle x2+y2−2x+y=5x^{2}+y^{2}- 2x + y = 5 meet at the point R(94,2)R\left( \frac{9}{4},2 \right), then the area of the triangle PQRPQR is

    Tap an option to check your answer.