Mathematics
In the given figure, PQ and PR are two equal chords of a circle. Show that the tangent at P is parallel to QR.
Answer
Given,
PQ = PR
∠PRQ = ∠PQR [Angles opposite to equal sides in a triangle are equal]
∠TPR = ∠PQR [Angles in alternate segment]
∴ ∠PRQ = ∠TPR
These are pair of alternate interior angles.
If the alternate interior angles are equal, then lines P and QR should be parallel.
Hence, proved tangent at P is parallel to QR.
Related Questions
In the given figure, PAT is tangent at A to the circle with centre O. If ∠ABC = 35°, find :
(i) ∠TAC
(ii) ∠PAB
In the given figure, PAT is tangent at A and BD is a diameter of the circle. If ∠ABD = 28° and ∠BDC = 52°, find :
(i) ∠TAD
(ii) ∠BAD
(iii) ∠PAB
(iv) ∠CBD
In the given figure, AB is a chord of the circle with centre O and BT is a tangent to the circle. If ∠OAB = 35°, find the values of x and y.
In the given figure, PAB is a secant to the circle and PT is a tangent at T. Prove that:
(i) ∠PAT ∼ ∠PTB
(ii) PA × PB = PT2
