Adv
deepaksoni
  • 0
Guru

Question 8. (a) In the figure (i) given below, AB is a diameter of the circle. If ∠ADC = 120°, find ∠CAB. (b) In the figure (ii) given below, sides AB and DC of a cyclic quadrilateral ABCD are produced to meet at E, the sides AD and BC are produced to meet at F. If x : y : z = 3 : 4 : 5, find the values of x, y and z.

  • 0

This is an important and exam oriented question from Chapter name- circles
Topic – Angle properties of circles
Chapter number- 15

In first qies AB is a diameter of the circle. If ∠ADC = 120°, we have to find ∠CAB.
In the figure (ii) , sides AB and DC of a cyclic quadrilateral ABCD are produced to meet at E, the sides AD and BC are produced to meet at F.   x : y : z = 3 : 4 : 5, now we have to find the values of x, y and z.
ICSE Avichal publication
Understanding ICSE Mathematics
Question 8

Share

1 Answer

  1. Solution:

    (a) Construction: Join BC, and AC then

    ABCD is a cyclic quadrilateral.

    ML Aggarwal Solutions for Class 10 Chapter 15 - Image 32

    Now in ∆DCF

    Ext. ∠2 = x + z

    and in ∆CBE

    Ext. ∠1 = x + y

    Adding (i) and (ii)

    x + y + x + z = ∠1 + ∠2

    2 x + y + z = 180o

    (ABCD is a cyclic quadrilateral)

    But x : y : z = 3 : 4 : 5

    x/y = ¾ (y = 4/3 x)

    x/z = 3/5 (z = 5/3 x.

    • 0
Leave an answer

Leave an answer

Browse

Choose from here the video type.

Put Video ID here: https://www.youtube.com/watch?v=sdUUx5FdySs Ex: "sdUUx5FdySs".

Captcha Click on image to update the captcha.

Related Questions