Question

If PA and PB are tangents to a circle with center o,radius 4 cm and PA is perpendicular to PB find the length of the tangents.

Answer 1

Answer:

CA is perpendicular to AP and CB is perpendicular to BP

Again AC = BC = 4 (radius of the circle)

Also AP = PB = (Tangents from point P)

So, BPAC is a square.

=> AP = PB = BC = CA = 4 cm

So, length of tangents are 4 cm each

Answer 2

Length of the tangents = 4cm

Given PA is perpendicular to PB

==> PA and PB are inclined at an angle of 90°

We know that tangents at the point of attachment is perpendicular to the radius.

Hence All the angles in the quadrilateral formed by the radii, and the 2 tangents PA And PB becomes 90°

And all the sides are equal as radii and tangents are equal.

Hence the quadrilateral is a SQUARE.

==> All the sides are equal

Therefore PA And PB are of the same length as the radii which is 4cm

A rough figure is given in the attachment