Mathematics
Prove that the tangents at the extremities of any chord make equal angles with the chord.
Answer
Let AB be a chord of a circle with centre O, and AP, BP be the tangents at A and B respectively.
From figure,
PA = PB [∵ Tangents from an external point to a circle are equal]
In triangle PAB,
∠PAB = ∠PBA [Angles opposite to equal sides in a triangle are equal]
∴ ∠PAC = ∠PBC.
Hence, proved any chord make equal angles with the chord.
Related Questions
In the given figure, PA and PB are tangents to a circle with centre O and ΔABC has been inscribed in the circle such that AB = AC. If ∠BAC = 72°, calculate
(i) ∠AOB
(ii) ∠APB.
Show that the tangent lines at the end points of a diameter of a circle are parallel.
Show that the line segment joining the points of contact of two parallel tangents passes through the centre.
In the given figure, PQ is a transverse common tangent to two circles with centres A and B and of radii 5 cm and 3 cm respectively. If PQ intersects AB at C such that CP = 12 cm, calculate AB.
