Question

In the figure , PAB is a secant and PT a tangent to the circle with centre O . if angle TAP =40°, PA = 9cm and AB=7cm.

Answer 1

Answer:

50 degrees

Step-by-step explanation:

Answer 2

$\mathbf{\angle TPA= 50^{\circ} \ and \ PT = 3\sqrt{7} (cm)}$

Step-by-step explanation:

• Given data

        PA = 9 cm

        AB = 7 cm

        $\mathbf{\angle ATP= 40^{\circ} }$         (please correct the question)

        Because angle made on any point on semicircle is 90° .

        So $\mathbf{\angle BAT= 90^{\circ}=\angle TAP }$

• In $\mathbf{\Delta PAT}$

         $\mathbf{\angle TAP+\angle ATP+\angle APT =180^{\circ}}$

         $\mathbf{90^{\circ}+40^{\circ} +\angle APT =180^{\circ}}$

         So on solving above equation

          $\mathbf{\angle APT =50^{\circ}}$

• By using Tangent secant theorem

         $\mathbf{PT^{2}=PA\times AB}$

         $\mathbf{PT^{2}=9\times 7}$

         $\mathbf{PT^{2}=3^2\times 7}$

         So

         $\mathbf{PT=3\sqrt{7} \ (cm)}$