# circle/tangent/chord..help!

• Feb 2nd 2010, 08:22 AM
snigdha
circle/tangent/chord..help!
In the figure AT is a tangent to the circle at A. TRP and AQ are parallel chords. AP and RQ intersect at C. If <ATP = 40, <APT=45, calculate
i) <ART
ii) <ACR.

i managed to get i) done...-

<RAT=<APR=45 ->[By alternate segment theorem]
Hence <ART= 180-(<ATR+<RAT)->[Sum of <s in △=180]
=180 - (40+45)
= 95.

Plz proceed after this to find <ACR....
• Feb 3rd 2010, 01:08 AM
Hello snigdha
Quote:

Originally Posted by snigdha
In the figure AT is a tangent to the circle at A. TRP and AQ are parallel chords. AP and RQ intersect at C. If <ATP = 40, <APT=45, calculate
i) <ART
ii) <ACR.

i managed to get i) done...-

<RAT=<APR=45 ->[By alternate segment theorem]
Hence <ART= 180-(<ATR+<RAT)->[Sum of <s in △=180]
=180 - (40+45)
= 95.

Plz proceed after this to find <ACR....

\$\displaystyle \angle PAQ = \angle RPA\$ (alternate angles)

\$\displaystyle \angle PAQ = \angle PRQ\$ (same segment)

Now look at the angles in \$\displaystyle \triangle CPR\$.