In figure , $P A$ and $P B$ are two tangents drawn from an external point $P$ to a circle with center $C$ and radius $4 c m$ . If $P A ⊥ P B$ , then find the length of each tangent.

Open in App

Solution

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

Suggest Corrections

Similar questions

PA and PB are two tangents drawn from an external point P to a circle with centre C and radius 4 cm. If PA & PB are perpendicular to each other, then the length of each tangent is:

Q. If two tangents PA and PB are drawn to a circle with centre O from an external point P (figure), then match the column.

From an external point P, tangents PA and PB are drawn to a circle with centre O. At one point E on the circle tangent is drawn, which intersects PA and PB at C and D respectively. If $P A = 14 c m$ , find the perimeter of $Δ P C D .$

Q. From an external point P, two tangents, PA and PB are drawn to a circle with centre O. At one point E on the circle tangent is drawn which intersects PA and PB at C and D, respectively. If PA = 10 cm, find the perimeter of the triangle PCD in cm.

Join BYJU'S Learning Program

In figure , PA and PB are two tangents drawn from an external point P to a circle with center C and radius 4 cm. If PA⊥PB, then find the length of each tangent.

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 cmSo, length of tangents are 4 cm each

In figure , $P A$ and $P B$ are two tangents drawn from an external point $P$ to a circle with center $C$ and radius $4 c m$ . If $P A ⊥ P B$ , then find the length of each tangent.

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