Question

Please explain the questions to me. thanks ​

Answer 1

5. a) 24

6. c) 9

Explanation:

Question 5:

Given:

`m\angle BMQ=42`

Arc BQ = 60°, Arc AP =
`x`°

Now, in order to find
`x`, we use the angle of intersecting chords theorem which says that the angle of intersecting chords is equal to the half of the sum of the angles of the intercepted arcs made by the intersecting chords. That is,

`m\angle BMQ=(1)/(2)( \overset{\frown}{AP}+\overset{\frown}{BQ})\\42=(1)/(2)(x+60)\\\textrm{Multplying both sides by 2}\\42* 2=x+60\\84=x+60\\x=84-60=24`

Therefore,
`x=24`. Option (a) is the correct answer.

Question 6:

Given:

AM = 6, BM = 6, PQ = 13, MQ = 'y', MQ > MP.

MP = PQ - MQ =
`13-y`

Now, in order to determine 'y', we use intersecting chords theorem which says that the product of the intersecting segments of two intersecting chords are always equal. That is,

`AM* BM=PM* MQ\\6* 6=(13-y)* y\\36=13y-y^2\\y^2-13y+36=0.......... (\textrm{Adding } y^2-13y\textrm{ both sides})\\(y-9)(y-4)=0\\y=9\ or\ y=4`

Now, in order to choose the correct value of 'y', we have to compare the lengths of MQ and MP.

For,
`y=4, MQ=4\ and\ MP=13-4=9` But, as per question, MQ > MP. So, we can't take 4 for 'y'.

Therefore, the correct answer is
`c) y=9`.