CBSE Class 10 Maths (Standard) 2015 · Paper 30/2/1 · Question 25

Circles 4 marks Hard

In Figure 4,

O

is the centre of the circle and

T P

is the tangent to the circle from an external point

T

. If

∠ P B T = 3 0^{\circ}

, prove that

B A : A T = 2 : 1

Figure 4

Answer

Since

∠ B P A = 9 0^{\circ}

gives

∠ P A B = 6 0^{\circ}

, and the tangent-chord angle

∠ T P A = 3 0^{\circ}

makes triangle PAT isosceles with

A T = A P = B A sin 3 0^{\circ} = \frac{1}{2} B A

, we get

B A : A T = 2 : 1

. Hence proved.

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