Question

In the given figuré, O is the centre of the circle and AP is a tangent at P. If angleAOP = 70°; then find angleOAP. ​

Answer 1

Answer:

it think 20°

Step-by-step explanation:

area of∆AOP,

ANGLE POA+OAP+APO=180°

we know that , radius of a circle two tangent is perpendicular to the tangent therefore angle equals to 90°

AOP 70 degree

poa equals to 90 degree.

therefore angle p o a =180-[70 + 90]

therefore 180 - 160 equal to 20.

therefore angle p o a equals to 20 degree

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Answer 2

Measure of the angle OAP is 20° if O is the centre of the circle , AP is a tangent  at P and m∠AOP = 70°

Given:

O is the center of the circle

AP is Tangent to the circle at P

m∠AOP = 70°

To Find:

m∠OAP = 70°

Solution:

Tangent Line to a Circle Theorem

A line is a tangent to a circle if and only if it is perpendicular to the radius at the point of tangency.

Triangle Angle Sum Theorem:

Sum of the Measures of the angles of a triangle is 180°

Step 1:

As AP is tangent to circle hence

m∠OPA = 90°

Step 2:

As OAP is a triangle hence sum of measures of the angles is 180°

m∠OPA + m∠AOP + m∠OAP = 180°

Step 3:

Substitute m∠OPA = 90°, m∠AOP = 70° in the equation and solve for m∠OAP

90° + 70° + m∠OAP = 180°

=> 160° + m∠OAP = 180°

=> m∠OAP = 180° - 160°

=> m∠OAP = 20°

Hence Measure of the angle OAP is 20°