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Length of Tangents Drawn from an External Point

From the figu...

Question

From the figure find the length of the tangent CD given AP = 3 cm, and PC = 8 cm.

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Solution

The given figure is:

We know that the lengths of the tangents from an external point to a circle are equal.

AP = PB = 3 cm and CD = BC

Since BC = PC – PB = 8 – 3 = 5 cm, CD = 5 cm

Hence, the length of CD is 5 cm.

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Similar questions

(i) In the given figure, 3 $\times$ CP = PD = 9 cm and AP = 4.5 cm. Find BP.

(ii) In the given figure, 5 $\times$ PA = 3 $\times$ AB = 30 cm and PC = 4 cm. Find CD.

(iii) In the given figure, tangent PT = 12.5 cm and PA =10 cm; find AB.

P A

P B

P

C D

Q

P A = 8 c m

C Q = 3 c m

P C

In the given figure, AC||QR and AB||PR.

What is the length of PC if DP = 8 cm, AP = 4 cm, and CR = 3.9 cm?

The given diagram shows two isosceles triangles which are similar also. In the given diagram, PQ and BC are not parallel and AP = PQ.

Given that PC =4 cm, AQ=3 cm, QB =12 cm, BC =15 cm.

Calculate the length of AP.

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