PQ is a chord of length 8 cm of a circle of radius 5 cm . The tangents at P and Q intersects at T. Find the length of TP.

20/3 cm

or 16.66 cm

To solve this problem, we can use the property that the lengths of tangents drawn from an external point to a circle are equal. Let's break down the steps to find the length of TP:

Step 1: Draw a circle with center O and radius 5 cm.
Step 2: Draw the chord PQ of length 8 cm.
Step 3: Draw tangents at points P and Q.
Step 4: Let the point of intersection of the tangents be T.
Step 5: Connect points P and T.

Now, let's find the length of TP:

Step 6: Since PQ is a chord, it divides the circle into two equal arcs.
Step 7: The length of each arc is half the circumference of the circle, which is πd.
Step 8: The diameter of the circle is twice the radius, which is 2 * 5 cm = 10 cm.
Step 9: Therefore, the length of each arc is π * 10 cm = 10π cm.
Step 10: Since PQ is 8 cm long, the remaining part of each arc is (10π - 8) cm.
Step 11: In triangle OTP, TP is the remaining part of the minor arc PQ.
Step 12: So, TP = (10π - 8) cm.

Hence, the length of TP is (10π - 8) cm.