P, Q, R and S are four points on a circle - Edexcel - GCSE Maths - Question 16 - 2022 - Paper 3
Question 16
P, Q, R and S are four points on a circle.
PX and SQ are straight lines.
Prove that triangle PQX and triangle SRV are similar.
Worked Solution & Example Answer:P, Q, R and S are four points on a circle - Edexcel - GCSE Maths - Question 16 - 2022 - Paper 3
Step 1
Prove that angle PQX = angle SRV
96%
114 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
By the Inscribed Angle Theorem, angles subtended by the same arc are equal. Angle PQX subtends arc PS and angle SRV also subtends the same arc PS. Therefore, we can conclude that:
∠PQX=∠SRV
Step 2
Prove that angle QPX = angle RXS
99%
104 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
Again, using the Inscribed Angle Theorem, angle QPX subtends arc QR and angle RXS subtends the same arc QR. Thus, we have:
∠QPX=∠RXS
Step 3
Prove that triangle PQX is similar to triangle SRV
96%
101 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
Since we have established that:
∠PQX=∠SRV
∠QPX=∠RXS
By the Angle-Angle (AA) criterion for triangle similarity, we conclude that triangle PQX is similar to triangle SRV.
